problem stringlengths 75 15.2k | answer stringlengths 1 34 | text_logic_form listlengths 1 11 | diagram_logic_form listlengths 0 456 | line_instances listlengths 1 110 | point_positions stringlengths 2 551 | circle_instances listlengths 0 4 |
|---|---|---|---|---|---|---|
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 10)
- Equals(LengthOf(Line(J, H)), x)
The area of $▱ A B C D$ is 150 square meters. The area of $▱ F G H J$ is 54 square meters. If $▱ A B C D \sim ▱ F G H J$, find the value of $x$. | 6 | [
"Equals(AreaOf(Parallelogram(A,B,C,D)),150)",
"Equals(AreaOf(Parallelogram(F,G,H,J)),54)",
"Similar(Parallelogram(A,B,C,D),Parallelogram(F,G,H,J))",
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(J, H)), x)"
] | [
"AD",
"BA",
"BC",
"CD",
"FG",
"FJ",
"GH",
"JH"
] | {"A": [35.0, 2.0], "B": [144.0, 1.0], "C": [109.0, 165.0], "D": [2.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(D, C)), x+4)
- Equals(LengthOf(Line(A, B)), 10)
- PointLiesOnLine(C, Line(D, A))
- PointLiesOnCircle(D, Circle(E, radius_4_0))
- PointLiesOnCircle(B, Circle(E, radius_4_0))
- PointLiesOnCircle(C, Circle(E, radius_4_0))
$\overline{AB}$ is tang... | 6.1 | [
"Tangent(Line(A,B),Circle($)). Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(D, C)), x+4)",
"Equals(LengthOf(Line(A, B)), 10)",
"PointLiesOnLine(C, Line(D, A))",
"PointLiesOnCircle(D, Circle(E, radius_4_0))",
"PointLiesOnCircle(B, Circle(E, radius_4_0))",
"PointLiesOnCircle(C, Circle(E, radius_4_0))"
] | [
"AB",
"AC",
"DA",
"DC"
] | {"A": [0.0, 72.0], "B": [191.0, 183.0], "C": [139.0, 73.0], "D": [326.0, 74.0], "E": [232.0, 98.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))
- Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))
- Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))
- Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))
- Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))
- Equals(Measure... | 57 | [
"Equals(MeasureOf(Angle(1)),123)",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(G, K, F)), MeasureOf(angle 16))",
"Equals(MeasureOf(Angle(F, K, A)), MeasureOf(angle 15))",
"Equals(MeasureOf(Angle(G, A, J)), MeasureOf(angle 14))",
"Equals(MeasureOf(Angle(H, K, G)), MeasureOf(angle 9))",
"Equals(MeasureOf(Angle(J, A, M)), MeasureOf(angle 13))",
"Equals(MeasureOf... | [
"AD",
"AG",
"AI",
"AJ",
"AK",
"AM",
"AO",
"AP",
"AQ",
"AS",
"AV",
"AW",
"BF",
"BH",
"BL",
"BT",
"BU",
"CE",
"CN",
"CR",
"DG",
"DK",
"DM",
"DO",
"DP",
"DV",
"DW",
"EN",
"ER",
"FH",
"FT",
"FU",
"GK",
"GM",
"GO",
"GP",
"GV",
"GW",
"HT",
"HU"... | {"A": [233.0, 125.0], "B": [87.0, 140.0], "C": [186.0, 219.0], "D": [152.0, 109.0], "E": [329.0, 259.0], "F": [86.0, 0.0], "G": [2.0, 64.0], "H": [85.0, 295.0], "I": [234.0, 307.0], "J": [233.0, 15.0], "K": [84.0, 87.0], "L": [118.0, 197.0], "M": [331.0, 158.0], "N": [0.0, 165.0], "O": [181.0, 116.0], "P": [136.0, 101.... | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(N, Line(X, Z))
- PointLiesOnLine(M, Line(X, Y))
- PointLiesOnLine(N, Line(C, D))
- PointLiesOnLine(M, Line(A, B))
- PointLiesOnCircle(Z, Circle(X, radius_0_0))
- PointLiesOnCircle(A, Circle(X, radius_0_0))
- PointLiesOnCircle(C, Circle(X, radius_0_0))
- PointLiesOnCircle(D, Circle(... | 15 | [
"Circle(X)",
"Equals(LengthOf(Line(A,B)),30)",
"Equals(LengthOf(Line(C,D)),30)",
"Equals(MeasureOf(Arc(C,Z)),40)",
"Find(LengthOf(Line(C,N)))"
] | [
"PointLiesOnLine(N, Line(X, Z))",
"PointLiesOnLine(M, Line(X, Y))",
"PointLiesOnLine(N, Line(C, D))",
"PointLiesOnLine(M, Line(A, B))",
"PointLiesOnCircle(Z, Circle(X, radius_0_0))",
"PointLiesOnCircle(A, Circle(X, radius_0_0))",
"PointLiesOnCircle(C, Circle(X, radius_0_0))",
"PointLiesOnCircle(D, Cir... | [
"AB",
"CD",
"MA",
"MB",
"NC",
"ND",
"XM",
"XN",
"XY",
"XZ",
"YM",
"ZN"
] | {"A": [35.0, 18.0], "B": [144.0, 32.0], "C": [78.0, 175.0], "D": [176.0, 100.0], "M": [96.0, 26.0], "N": [128.0, 137.0], "X": [90.0, 91.0], "Y": [98.0, 0.0], "Z": [143.0, 156.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, A)), 15)
- Equals(MeasureOf(Angle(B, D, E)), 82)
- Equals(LengthOf(Line(E, F)), 9.2)
- PointLiesOnLine(F, Line(C, A))
- PointLiesOnLine(E, Line(C, B))
- PointLiesOnLine(D, Line(B, A))
Find $DE$. | 7.5 | [
"Find(LengthOf(Line(D,E)))"
] | [
"Equals(LengthOf(Line(C, A)), 15)",
"Equals(MeasureOf(Angle(B, D, E)), 82)",
"Equals(LengthOf(Line(E, F)), 9.2)",
"PointLiesOnLine(F, Line(C, A))",
"PointLiesOnLine(E, Line(C, B))",
"PointLiesOnLine(D, Line(B, A))"
] | [
"BD",
"BA",
"CB",
"CF",
"CA",
"DA",
"EB",
"EC",
"ED",
"EF",
"FA"
] | {"B": [564.0, 320.0], "C": [75.0, 319.0], "D": [395.0, 183.0], "E": [313.0, 319.0], "F": [152.0, 182.0], "A": [226.0, 48.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(K, Line(E, G))
- PointLiesOnLine(K, Line(H, F))
- Perpendicular(Line(H, E), Line(H, G))
Quadrilateral EFGH is a rectangle. If $m\angle FEG = 57$, find $m\angle GEH$. | 33 | [
"Rectangle(E,F,G,H)",
"Equals(MeasureOf(Angle(F,E,G)),57)",
"Find(MeasureOf(Angle(G,E,H)))"
] | [
"PointLiesOnLine(K, Line(E, G))",
"PointLiesOnLine(K, Line(H, F))",
"Perpendicular(Line(H, E), Line(H, G))"
] | [
"EF",
"EG",
"EH",
"EK",
"FK",
"GF",
"GH",
"GK",
"HK"
] | {"E": [0.0, 0.0], "F": [341.0, 2.0], "G": [343.0, 163.0], "H": [2.0, 164.0], "K": [173.0, 83.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, W)), 4)
- Equals(MeasureOf(Angle(W, A, R)), l)
- Equals(LengthOf(Line(R, W)), 4)
- Equals(MeasureOf(Angle(W, A, R)), n)
- Equals(MeasureOf(Angle(W, A, R)), w)
- Equals(LengthOf(Line(W, L)), 8)
- Equals(LengthOf(Line(W, L)), 12)
- PointLiesOnLine(L, Line(R, W))
Find $x$. | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, W)), 4)",
"Equals(MeasureOf(Angle(W, A, R)), l)",
"Equals(LengthOf(Line(R, W)), 4)",
"Equals(MeasureOf(Angle(W, A, R)), n)",
"Equals(MeasureOf(Angle(W, A, R)), w)",
"Equals(LengthOf(Line(W, L)), 8)",
"Equals(LengthOf(Line(W, L)), 12)",
"PointLiesOnLine(L, Line(R, W))"
] | [
"AR",
"AW",
"RL",
"RW",
"WL"
] | {"A": [276.0, 14.0], "L": [159.0, 137.0], "R": [2.0, 13.0], "W": [282.0, 236.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 4)
- Equals(LengthOf(Line(B, E)), 3)
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(E, Line(C, A))
If $ABCD$ is a kite, find $AB$ | 5 | [
"Kite(A,B,C,D)",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(A, E)), 4)",
"Equals(LengthOf(Line(B, E)), 3)",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(E, Line(C, A))"
] | [
"AE",
"BA",
"BC",
"BD",
"BE",
"CA",
"CE",
"DA",
"DC",
"DE"
] | {"A": [145.0, 1.0], "B": [218.0, 85.0], "C": [144.0, 168.0], "D": [0.0, 84.0], "E": [144.0, 85.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 21)
- Equals(LengthOf(Line(A, C)), 3x-6)
- PointLiesOnLine(B, Line(C, D))
- Equals(LengthOf(Line(B, D)), LengthOf(Line(B, C)))
- Equals(LengthOf(Line(E, H)), 14)
- Equals(LengthOf(Line(E, G)), x+4)
- PointLiesOnLine(F, Line(G, H))
- Equals(LengthOf(Line(H, F)), LengthO... | 8 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 21)",
"Equals(LengthOf(Line(A, C)), 3x-6)",
"PointLiesOnLine(B, Line(C, D))",
"Equals(LengthOf(Line(B, D)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(E, H)), 14)",
"Equals(LengthOf(Line(E, G)), x+4)",
"PointLiesOnLine(F, Line(G, H))",
"Equals(LengthOf(Line(H, F)), Len... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD",
"EF",
"EG",
"EH",
"FG",
"HF",
"HG"
] | {"A": [30.0, 156.0], "B": [82.0, 84.0], "C": [171.0, 157.0], "D": [1.0, 3.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 3y-8)
- Equals(MeasureOf(Angle(F, B, A)), 20)
- Equals(LengthOf(Line(A, D)), 13)
- Equals(LengthOf(Line(C, B)), 2x+7)
- Equals(MeasureOf(Angle(B, F, C)), 49)
- Equals(MeasureOf(Angle(A, D, F)), 59)
- Equals(LengthOf(Line(C, D)), 10)
- PointLiesOnLine(F, Line(A, C))
- P... | 131 | [
"Parallelogram(A,B,C,D)",
"Find(MeasureOf(Angle(A,F,B)))"
] | [
"Equals(LengthOf(Line(A, B)), 3y-8)",
"Equals(MeasureOf(Angle(F, B, A)), 20)",
"Equals(LengthOf(Line(A, D)), 13)",
"Equals(LengthOf(Line(C, B)), 2x+7)",
"Equals(MeasureOf(Angle(B, F, C)), 49)",
"Equals(MeasureOf(Angle(A, D, F)), 59)",
"Equals(LengthOf(Line(C, D)), 10)",
"PointLiesOnLine(F, Line(A, C))... | [
"AC",
"AD",
"AB",
"AF",
"CD",
"CB",
"CF",
"DB",
"DF",
"BF"
] | {"A": [97.31243783713673, 1.3959393100317925], "C": [296.2613185887417, 239.18904318857386], "D": [0.6777316735823149, 240.0], "B": [391.78928168839576, 0.6027205312470016], "F": [196.76472404260394, 119.72046420903439]} | [] |
Diagram Logic Form:
- PointLiesOnLine(Y, Line(X, Z))
- PointLiesOnLine(W, Line(D, Y))
- PointLiesOnLine(W, Line(D, T))
- PointLiesOnLine(Y, Line(D, T))
- PointLiesOnLine(Y, Line(W, T))
- Perpendicular(Line(X, Y), Line(Y, W))
- Equals(LengthOf(Line(X, Y)), LengthOf(Line(Y, Z)))
If $WZ=25.3$, $YZ=22.4$, $WZ=25.3$, find ... | 22.4 | [
"Equals(LengthOf(Line(W,Z)),25.3)",
"Equals(LengthOf(Line(Y,Z)),22.4)",
"Find(LengthOf(Line(X,Y)))"
] | [
"PointLiesOnLine(Y, Line(X, Z))",
"PointLiesOnLine(W, Line(D, Y))",
"PointLiesOnLine(W, Line(D, T))",
"PointLiesOnLine(Y, Line(D, T))",
"PointLiesOnLine(Y, Line(W, T))",
"Perpendicular(Line(X, Y), Line(Y, W))",
"Equals(LengthOf(Line(X, Y)), LengthOf(Line(Y, Z)))"
] | [
"DW",
"WY",
"YT",
"DY",
"WT",
"DT",
"XY",
"YZ",
"XZ",
"WX",
"WZ"
] | {"D": [0.0, 182.0], "T": [291.0, 182.0], "W": [100.0, 171.0], "X": [226.0, -0.0], "Y": [226.0, 182.0], "Z": [226.0, 361.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, F, E)), 108)
- Equals(MeasureOf(Angle(B, C, E)), 120)
- Equals(MeasureOf(Angle(D, B, C)), 5y)
- Equals(MeasureOf(Angle(F, D, B)), 2x)
- PointLiesOnLine(F, Line(C, E))
- Parallel(Line(B, D), Line(C, E))
Find the value of the variable $y$ in the figure. | 12 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(D, F, E)), 108)",
"Equals(MeasureOf(Angle(B, C, E)), 120)",
"Equals(MeasureOf(Angle(D, B, C)), 5y)",
"Equals(MeasureOf(Angle(F, D, B)), 2x)",
"PointLiesOnLine(F, Line(C, E))",
"Parallel(Line(B, D), Line(C, E))"
] | [
"BC",
"BD",
"CE",
"CF",
"DF",
"FE"
] | {"B": [1.0, 3.0], "C": [129.0, 226.0], "D": [275.0, 1.0], "E": [495.0, 226.0], "F": [350.0, 228.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Z, Line(Y, W))
- PointLiesOnLine(V, Line(U, S))
- PointLiesOnLine(Z, Line(R, X))
- PointLiesOnLine(V, Line(R, T))
- PointLiesOnCircle(Y, Circle(R, radius_5_0))
- PointLiesOnCircle(U, Circle(R, radius_5_0))
- PointLiesOnCircle(S, Circle(R, radius_5_0))
- PointLiesOnCircle(W, Circle(... | 10 | [
"Circle(R)",
"Equals(LengthOf(Line(S,U)),20)",
"Equals(LengthOf(Line(Y,W)),20)",
"Equals(MeasureOf(Arc(Y,X)),45)",
"Find(LengthOf(Line(U,V)))"
] | [
"PointLiesOnLine(Z, Line(Y, W))",
"PointLiesOnLine(V, Line(U, S))",
"PointLiesOnLine(Z, Line(R, X))",
"PointLiesOnLine(V, Line(R, T))",
"PointLiesOnCircle(Y, Circle(R, radius_5_0))",
"PointLiesOnCircle(U, Circle(R, radius_5_0))",
"PointLiesOnCircle(S, Circle(R, radius_5_0))",
"PointLiesOnCircle(W, Cir... | [
"RT",
"RX",
"US",
"VR",
"VS",
"VT",
"VU",
"YW",
"YZ",
"ZR",
"ZW",
"ZX"
] | {"R": [100.0, 97.0], "S": [106.0, 0.0], "T": [178.0, 39.0], "U": [195.0, 121.0], "V": [150.0, 60.0], "W": [141.0, 186.0], "X": [61.0, 188.0], "Y": [7.0, 128.0], "Z": [74.0, 157.0]} | [
"R"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(P, N, M)), MeasureOf(Angle(P, Q, M)))
- Equals(MeasureOf(Angle(Q, P, N)), MeasureOf(Angle(Q, M, N)))
parallelogram MNPQ with $m \angle M=10 x$ and $m \angle N=20 x$, find $\angle Q$ | 120 | [
"Parallelogram(M,N,P,Q)",
"Equals(MeasureOf(Angle(M)),10x)",
"Equals(MeasureOf(Angle(N)),20x)",
"Find(MeasureOf(Angle(N)))"
] | [
"Equals(MeasureOf(Angle(P, N, M)), MeasureOf(Angle(P, Q, M)))",
"Equals(MeasureOf(Angle(Q, P, N)), MeasureOf(Angle(Q, M, N)))"
] | [
"NM",
"PN",
"PQ",
"QM"
] | {"M": [1.0, 0.0], "N": [197.0, 2.0], "P": [255.0, 104.0], "Q": [59.0, 104.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, A)), x)
- Equals(LengthOf(Line(U, C)), x)
- Equals(LengthOf(Line(S, A)), 3)
- Equals(LengthOf(Line(R, D)), 3)
- PointLiesOnLine(C, Line(U, R))
- PointLiesOnLine(B, Line(U, T))
- PointLiesOnLine(A, Line(T, S))
- PointLiesOnLine(D, Line(R, S))
- PointLiesOnCircle(D, Circle(J,... | 1.5 | [
"CircumscribedTo(Quadrilateral(R,S,T,U),Circle(J))",
"Equals(PerimeterOf(Polygon($)),18)",
"Find(x)"
] | [
"Equals(LengthOf(Line(T, A)), x)",
"Equals(LengthOf(Line(U, C)), x)",
"Equals(LengthOf(Line(S, A)), 3)",
"Equals(LengthOf(Line(R, D)), 3)",
"PointLiesOnLine(C, Line(U, R))",
"PointLiesOnLine(B, Line(U, T))",
"PointLiesOnLine(A, Line(T, S))",
"PointLiesOnLine(D, Line(R, S))",
"PointLiesOnCircle(D, Ci... | [
"BG",
"RD",
"RJ",
"RS",
"SA",
"SD",
"TA",
"TB",
"TG",
"TS",
"UB",
"UG",
"UJ",
"UR",
"UT"
] | {"A": [45.0, 104.0], "B": [173.0, 4.0], "C": [309.0, 104.0], "D": [177.0, 276.0], "J": [178.0, 139.0], "R": [354.0, 277.0], "S": [0.0, 277.0], "T": [70.0, 1.0], "U": [284.0, 2.0]} | [
"J"
] |
Diagram Logic Form:
- PointLiesOnLine(L, Line(T, R))
- PointLiesOnLine(W, Line(R, S))
- Parallel(Line(T, S), Line(L, W))
If TR = 8, LR = 3, and RW = 6, find WS. | 10 | [
"Equals(LengthOf(Line(T,R)),8)",
"Equals(LengthOf(Line(L,R)),3)",
"Equals(LengthOf(Line(R,W)),6)",
"Find(LengthOf(Line(W,S)))"
] | [
"PointLiesOnLine(L, Line(T, R))",
"PointLiesOnLine(W, Line(R, S))",
"Parallel(Line(T, S), Line(L, W))"
] | [
"LW",
"RL",
"RS",
"RW",
"SW",
"TL",
"TR",
"TS"
] | {"L": [90.0, 43.0], "R": [1.0, 114.0], "S": [289.0, 86.0], "T": [142.0, 1.0], "W": [182.0, 97.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 12)
- Equals(LengthOf(Line(B, C)), y)
- Equals(LengthOf(Line(B, D)), x)
- Equals(LengthOf(Line(A, C)), 10)
- Equals(LengthOf(Line(C, D)), z)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(A, B), Line(B, C))
- Perpendicular(Line(B, D), Line(A, D))
Find z. | \frac { 22 } { 5 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, B)), 12)",
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(B, D)), x)",
"Equals(LengthOf(Line(A, C)), 10)",
"Equals(LengthOf(Line(C, D)), z)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(A, B), Line(B, C))",
"Perpendicular(Line(B, D), Line(A, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [361.0, 167.0], "B": [113.33553257765855, 1.554793631565289], "C": [0.0, 167.0], "D": [110.0, 167.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 8)
- Equals(LengthOf(Line(A, C)), 12)
- PointLiesOnLine(D, Line(B, C))
- PointLiesOnCircle(A, Circle(D, radius_1_0))
- PointLiesOnCircle(B, Circle(D, radius_1_0))
- PointLiesOnCircle(C, Circle(D, radius_1_0))
The triangle is inscribed in $\odot D$. Find the exact circ... | 4 \sqrt { 13 } \pi | [
"InscribedIn(Triangle($),Circle(D))",
"Find(CircumferenceOf(Circle(D)))"
] | [
"Equals(LengthOf(Line(B, A)), 8)",
"Equals(LengthOf(Line(A, C)), 12)",
"PointLiesOnLine(D, Line(B, C))",
"PointLiesOnCircle(A, Circle(D, radius_1_0))",
"PointLiesOnCircle(B, Circle(D, radius_1_0))",
"PointLiesOnCircle(C, Circle(D, radius_1_0))"
] | [
"AB",
"AC",
"BC",
"BD",
"CD"
] | {"A": [307.0, 258.0], "B": [305.0, 77.0], "C": [28.0, 260.0], "D": [163.0, 171.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 4)
- Equals(LengthOf(Line(A, C)), 9)
- Equals(LengthOf(Line(A, E)), x)
- Equals(LengthOf(Line(B, E)), 8)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(A, Line(B, F))
- PointLiesOnLine(E, Line(B, F))
- PointLiesOnLine(A, Line(C, D))
- PointLiesOnLine(A, Line(E, F))... | 5.3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 4)",
"Equals(LengthOf(Line(A, C)), 9)",
"Equals(LengthOf(Line(A, E)), x)",
"Equals(LengthOf(Line(B, E)), 8)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(A, Line(B, F))",
"PointLiesOnLine(E, Line(B, F))",
"PointLiesOnLine(A, Line(C, D))",
"PointLiesOnLine(A, Line... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"BE",
"BF",
"CD",
"DF",
"EF"
] | {"A": [106.0, 48.0], "B": [106.0, 210.0], "C": [1.0, 105.0], "D": [168.0, 19.0], "E": [108.0, 107.0], "F": [105.0, -0.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, Q)), 6)
- Equals(LengthOf(Line(P, Q)), 2x+1)
- Equals(LengthOf(Line(S, T)), 4)
- Equals(LengthOf(Line(P, T)), 10)
- PointLiesOnLine(T, Line(S, P))
- PointLiesOnLine(Q, Line(R, P))
- Perpendicular(Line(R, S), Line(Q, T))
Find PQ | 15 | [
"Find(LengthOf(Line(P,Q)))"
] | [
"Equals(LengthOf(Line(R, Q)), 6)",
"Equals(LengthOf(Line(P, Q)), 2x+1)",
"Equals(LengthOf(Line(S, T)), 4)",
"Equals(LengthOf(Line(P, T)), 10)",
"PointLiesOnLine(T, Line(S, P))",
"PointLiesOnLine(Q, Line(R, P))",
"Perpendicular(Line(R, S), Line(Q, T))"
] | [
"PQ",
"PT",
"RP",
"RQ",
"SP",
"SR",
"ST",
"TQ"
] | {"P": [332.0, 196.0], "Q": [100.0, 60.0], "R": [0.0, 1.0], "S": [50.0, 189.0], "T": [133.0, 191.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, F)), x)
- Equals(LengthOf(Line(B, D)), 3)
- Equals(LengthOf(Line(C, F)), 5)
- Equals(LengthOf(Line(A, D)), 9)
- PointLiesOnLine(D, Line(A, B))
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(E, Line(A, D))
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnLine(D, Line(B, E))... | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, F)), x)",
"Equals(LengthOf(Line(B, D)), 3)",
"Equals(LengthOf(Line(C, F)), 5)",
"Equals(LengthOf(Line(A, D)), 9)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(D, Line... | [
"AB",
"AD",
"AE",
"BC",
"BD",
"BE",
"BF",
"CF",
"DE"
] | {"A": [43.0, 213.0], "B": [181.0, 1.0], "C": [7.0, 98.0], "D": [146.0, 55.0], "E": [96.0, 135.0], "F": [108.0, 41.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, A, B)), x)
- Equals(MeasureOf(Angle(A, D, C)), 100)
- Equals(MeasureOf(Angle(A, B, C)), 42)
- PointLiesOnLine(D, Line(B, C))
Find $x$. | 58 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, A, B)), x)",
"Equals(MeasureOf(Angle(A, D, C)), 100)",
"Equals(MeasureOf(Angle(A, B, C)), 42)",
"PointLiesOnLine(D, Line(B, C))"
] | [
"AB",
"AD",
"BC",
"BD",
"DC"
] | {"A": [204.0, 1.0], "B": [2.0, 184.0], "C": [312.0, 185.0], "D": [237.0, 185.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(U, R)), 16)
- Equals(LengthOf(Line(V, R)), 11.2)
- Equals(LengthOf(Line(V, S)), 7)
- Equals(LengthOf(Line(U, S)), x)
- PointLiesOnLine(S, Line(V, U))
$\overline{RS}$ bisects $\angle VRU$. Solve for $x$. | 10 | [
"BisectsAngle(Line(R,S),Angle(V,R,U))",
"Find(x)"
] | [
"Equals(LengthOf(Line(U, R)), 16)",
"Equals(LengthOf(Line(V, R)), 11.2)",
"Equals(LengthOf(Line(V, S)), 7)",
"Equals(LengthOf(Line(U, S)), x)",
"PointLiesOnLine(S, Line(V, U))"
] | [
"RS",
"UR",
"US",
"VR",
"VS",
"VU"
] | {"R": [198.0, 1.0], "S": [263.0, 186.0], "U": [592.0, 186.0], "V": [0.0, 186.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, D)), 75)
- Equals(MeasureOf(Angle(C, A, E)), 28)
- Equals(MeasureOf(Angle(B, E, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, E, B)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(B, D, A)), 35)
- Equals(MeasureOf(Angle(E, C, A)), MeasureOf(angle 3))
- PointLiesO... | 110 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(C, B, D)), 75)",
"Equals(MeasureOf(Angle(C, A, E)), 28)",
"Equals(MeasureOf(Angle(B, E, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, E, B)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(B, D, A)), 35)",
"Equals(MeasureOf(Angle(E, C, A)), MeasureOf(angle 3))",
"PointLies... | [
"AC",
"AD",
"AE",
"CB",
"CE",
"DB",
"DE",
"EB"
] | {"A": [620.7386922629854, 1.0262194500865718], "B": [170.51390073911983, 0.21619505535871042], "C": [392.14561979742626, 267.10858214908586], "D": [0.0, 242.0], "E": [281.1403667596228, 133.06940773461562]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(H, F)), 17)
- Equals(LengthOf(Line(F, G)), 9x-6)
- Equals(LengthOf(Line(H, G)), 7x+4)
- Equals(LengthOf(Line(F, G)), LengthOf(Line(H, G)))
Find $x$ | 5 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(H, F)), 17)",
"Equals(LengthOf(Line(F, G)), 9x-6)",
"Equals(LengthOf(Line(H, G)), 7x+4)",
"Equals(LengthOf(Line(F, G)), LengthOf(Line(H, G)))"
] | [
"FG",
"HF",
"HG"
] | {"F": [2.0, 2.0], "G": [106.0, 158.0], "H": [281.0, 158.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, X)), x)
- Equals(LengthOf(Line(B, X)), 5)
- Equals(LengthOf(Line(A, B)), 4)
- Equals(LengthOf(Line(A, D)), 7)
- PointLiesOnLine(C, Line(A, D))
- PointLiesOnLine(A, Line(C, B))
- PointLiesOnLine(A, Line(B, D))
- PointLiesOnLine(C, Line(B, D))
- PointLiesOnLine(X, Line(B, F))... | 3.8 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(F, X)), x)",
"Equals(LengthOf(Line(B, X)), 5)",
"Equals(LengthOf(Line(A, B)), 4)",
"Equals(LengthOf(Line(A, D)), 7)",
"PointLiesOnLine(C, Line(A, D))",
"PointLiesOnLine(A, Line(C, B))",
"PointLiesOnLine(A, Line(B, D))",
"PointLiesOnLine(C, Line(B, D))",
"PointLiesOnLine(X, Line... | [
"AB",
"AC",
"AD",
"BD",
"BF",
"BX",
"CB",
"CD",
"XF"
] | {"A": [105.0, 40.0], "B": [157.0, 6.0], "C": [59.0, 67.0], "D": [9.0, 98.0], "F": [20.0, 18.0], "X": [86.0, 13.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, E)), 98)
- Equals(MeasureOf(Angle(A, D, C)), 40)
- PointLiesOnLine(A, Line(C, E))
- PointLiesOnLine(A, Line(D, F))
- PointLiesOnLine(B, Line(D, F))
- PointLiesOnLine(B, Line(D, A))
- PointLiesOnLine(A, Line(F, B))
- PointLiesOnCircle(C, Circle(B, radius_5_0))
- PointLi... | 80 | [
"Find(MeasureOf(Arc(C,F)))"
] | [
"Equals(MeasureOf(Angle(B, A, E)), 98)",
"Equals(MeasureOf(Angle(A, D, C)), 40)",
"PointLiesOnLine(A, Line(C, E))",
"PointLiesOnLine(A, Line(D, F))",
"PointLiesOnLine(B, Line(D, F))",
"PointLiesOnLine(B, Line(D, A))",
"PointLiesOnLine(A, Line(F, B))",
"PointLiesOnCircle(C, Circle(B, radius_5_0))",
"... | [
"AB",
"AF",
"CA",
"CD",
"CE",
"DA",
"DB",
"DF",
"EA",
"FB"
] | {"A": [149.0, 177.0], "B": [152.0, 155.0], "C": [4.0, 178.0], "D": [151.0, 3.0], "E": [299.0, 178.0], "F": [149.0, 303.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), c)
- Equals(MeasureOf(Angle(A, B, C)), 60)
- Equals(LengthOf(Line(C, B)), a)
- Equals(MeasureOf(Angle(C, A, B)), 30)
- Equals(LengthOf(Line(C, A)), b)
- Perpendicular(Line(C, B), Line(C, A))
If $b=18,$ find $c$ | 12 \sqrt { 3 } | [
"Equals(b,18)",
"Find(c)"
] | [
"Equals(LengthOf(Line(A, B)), c)",
"Equals(MeasureOf(Angle(A, B, C)), 60)",
"Equals(LengthOf(Line(C, B)), a)",
"Equals(MeasureOf(Angle(C, A, B)), 30)",
"Equals(LengthOf(Line(C, A)), b)",
"Perpendicular(Line(C, B), Line(C, A))"
] | [
"AB",
"CA",
"CB"
] | {"A": [262.0, 96.0], "B": [0.0, 0.0], "C": [2.0, 96.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(H, F)), 6x+1)
- Equals(LengthOf(Line(G, F)), 3x+10)
- Equals(LengthOf(Line(H, G)), 9x-8)
$\triangle FGH$ is an equilateral triangle. Find $FG$. | 19 | [
"Equilateral(Triangle(F,G,H))",
"Triangle($)",
"Find(LengthOf(Line(H,G)))"
] | [
"Equals(LengthOf(Line(H, F)), 6x+1)",
"Equals(LengthOf(Line(G, F)), 3x+10)",
"Equals(LengthOf(Line(H, G)), 9x-8)"
] | [
"GF",
"HF",
"HG"
] | {"F": [227.0, 2.0], "G": [453.0, 326.0], "H": [0.0, 325.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, C, O)), 60)
- Equals(LengthOf(Line(C, O)), 20)
- Equals(LengthOf(Line(B, O)), 15)
- PointLiesOnLine(E, Line(C, A))
- Perpendicular(Line(O, E), Line(E, A))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 259.8 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(MeasureOf(Angle(E, C, O)), 60)",
"Equals(LengthOf(Line(C, O)), 20)",
"Equals(LengthOf(Line(B, O)), 15)",
"PointLiesOnLine(E, Line(C, A))",
"Perpendicular(Line(O, E), Line(E, A))"
] | [
"AB",
"AC",
"BO",
"CO",
"AE",
"CE",
"OE"
] | {"A": [143.0, 0.0], "B": [218.0, 177.0], "C": [1.0, 2.0], "O": [75.0, 177.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, G, C)), 3x)
- Equals(MeasureOf(Angle(C, G, H)), 42)
- Equals(MeasureOf(Angle(G, C, D)), z)
- Equals(MeasureOf(Angle(G, C, H)), 48)
- Equals(MeasureOf(Angle(G, H, C)), y)
- Parallel(Line(G,D), Line(H,C))
-
Find $y$ in the figure. | 90 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(D, G, C)), 3x)",
"Equals(MeasureOf(Angle(C, G, H)), 42)",
"Equals(MeasureOf(Angle(G, C, D)), z)",
"Equals(MeasureOf(Angle(G, C, H)), 48)",
"Equals(MeasureOf(Angle(G, H, C)), y)",
"Parallel(Line(G,D), Line(H,C))",
""
] | [
"DC",
"GC",
"GD",
"HC",
"HG"
] | {"A": [203.0, 109.0], "B": [7.0, 133.0], "C": [197.0, 218.0], "D": [196.0, 8.0], "E": [98.0, 8.0], "F": [97.0, 217.0], "G": [8.0, 9.0], "H": [8.0, 217.0], "I": [8.0, 171.0], "J": [8.0, 58.0], "K": [198.0, 65.0], "L": [11.0, 101.0], "M": [196.0, 192.0], "N": [196.0, 120.0], "O": [196.0, 84.0], "P": [7.0, 115.0], "Q": [1... | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(W, A))
- PointLiesOnLine(X, Line(W, P))
- PointLiesOnLine(P, Line(H, A))
- PointLiesOnLine(X, Line(H, Q))
-
If $\overline{W P}$ is a median and an angle bisector, $A P=3 y+11$, $P H=7 y-5$, $m \angle H W P=x+12$, $m \angle P A W=3 x-2$, and $m \angle H W A=4 x-16$, find $... | 20 | [
"IsMedianOf(Line(W,P),Shape($))",
"BisectsAngle(Line(W,P),Angle($))",
"Equals(LengthOf(Line(A,P)),3y+11)",
"Equals(LengthOf(Line(P,H)),7y-5)",
"Equals(MeasureOf(Angle(H,W,P)),x+12)",
"Equals(MeasureOf(Angle(P,A,W)),3x-2)",
"Equals(MeasureOf(Angle(H,W,A)),4x-16)",
"Find(x)"
] | [
"PointLiesOnLine(Q, Line(W, A))",
"PointLiesOnLine(X, Line(W, P))",
"PointLiesOnLine(P, Line(H, A))",
"PointLiesOnLine(X, Line(H, Q))",
""
] | [
"HA",
"HP",
"HQ",
"PA",
"QA",
"WA",
"WH",
"WP",
"WQ",
"XH",
"XP",
"XQ",
"XW"
] | {"A": [210.0, 125.0], "H": [134.0, 1.0], "P": [172.0, 63.0], "Q": [161.0, 136.0], "W": [1.0, 167.0], "X": [148.0, 77.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(M, Line(P, L))
- PointLiesOnLine(A, Line(P, K))
- PointLiesOnLine(B, Line(J, L))
- PointLiesOnLine(K, Line(J, L))
- PointLiesOnLine(A, Line(J, M))
- PointLiesOnLine(K, Line(J, B))
- PointLiesOnLine(B, Line(L, K))
In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. ... | 32 | [
"Triangle(J,L,P)",
"Equals(MeasureOf(Angle(J,M,P)),3x-6)",
"Equals(LengthOf(Line(J,K)),3y-2)",
"Equals(LengthOf(Line(L,K)),5y-8)",
"Equals(Line(J,M),AltitudeOf(Triangle(J,L,P)))",
"Find(x)"
] | [
"PointLiesOnLine(M, Line(P, L))",
"PointLiesOnLine(A, Line(P, K))",
"PointLiesOnLine(B, Line(J, L))",
"PointLiesOnLine(K, Line(J, L))",
"PointLiesOnLine(A, Line(J, M))",
"PointLiesOnLine(K, Line(J, B))",
"PointLiesOnLine(B, Line(L, K))"
] | [
"PA",
"PJ",
"PL",
"PM",
"PK",
"AJ",
"AM",
"AB",
"AK",
"JL",
"JM",
"JB",
"JK",
"LM",
"LB",
"LK",
"KB"
] | {"P": [454.711070060208, 232.5], "A": [218.4277368554737, 124.999618999238], "J": [0.5731301538313289, 232.5], "L": [330.5068980729884, 2.5333361343913907], "M": [359.34080869860685, 55.325933476799946], "B": [203.66880616174583, 89.21566110397947], "K": [178.83448549410699, 106.9244390299184]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), 7)
- Equals(MeasureOf(Angle(A, D, B)), 196)
- PointLiesOnLine(A, Line(D, E))
- PointLiesOnLine(B, Line(D, F))
- PointLiesOnCircle(A, Circle(C, radius_2_0))
- PointLiesOnCircle(B, Circle(C, radius_2_0))
- PointLiesOnCircle(D, Circle(C, radius_2_0))
Find $\angle 7$ | 98 | [
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(LengthOf(Line(D, B)), 7)",
"Equals(MeasureOf(Angle(A, D, B)), 196)",
"PointLiesOnLine(A, Line(D, E))",
"PointLiesOnLine(B, Line(D, F))",
"PointLiesOnCircle(A, Circle(C, radius_2_0))",
"PointLiesOnCircle(B, Circle(C, radius_2_0))",
"PointLiesOnCircle(D, Circle(C, radius_2_0))"
] | [
"AD",
"AE",
"BF",
"DB",
"DE",
"DF"
] | {"A": [127.0, 58.0], "B": [21.0, 49.0], "C": [77.0, 53.0], "D": [39.0, 19.0], "E": [158.0, 71.0], "F": [2.0, 75.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, B, C)), 35)
- Equals(LengthOf(Line(A, C)), 12)
- Equals(LengthOf(Line(C, E)), 4)
- PointLiesOnLine(C, Line(A, E))
- Perpendicular(Line(B, E), Line(E, C))
Find the area of the figure. Round to the nearest hundredth, if necessary. | 68.6 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(MeasureOf(Angle(E, B, C)), 35)",
"Equals(LengthOf(Line(A, C)), 12)",
"Equals(LengthOf(Line(C, E)), 4)",
"PointLiesOnLine(C, Line(A, E))",
"Perpendicular(Line(B, E), Line(E, C))"
] | [
"AC",
"AD",
"AE",
"CB",
"CE",
"DB",
"EC"
] | {"A": [466.0, 166.0], "B": [0.0, 0.0], "C": [118.0, 166.0], "D": [351.0, 2.0], "E": [105.0, 165.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), z)
- Equals(LengthOf(Line(B, Y)), 15)
- Equals(LengthOf(Line(A, C)), 5)
- PointLiesOnLine(Y, Line(B, C))
- Perpendicular(Line(B, Y), Line(A, Y))
- Perpendicular(Line(A, B), Line(A, C))
Find z | 10 \sqrt { 2 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, B)), z)",
"Equals(LengthOf(Line(B, Y)), 15)",
"Equals(LengthOf(Line(A, C)), 5)",
"PointLiesOnLine(Y, Line(B, C))",
"Perpendicular(Line(B, Y), Line(A, Y))",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"AY",
"BC",
"BY",
"CY"
] | {"A": [1.0, 218.0], "B": [78.0, 0.0], "C": [78.0, 247.0], "Y": [79.0, 220.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, E)), 33)
- Equals(MeasureOf(Arc(C, B)), x)
- Equals(MeasureOf(Arc(D, E)), 51)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(D, Line(A, C))
- PointLiesOnCircle(B, Circle(F, radius_5_0))
- PointLiesOnCircle(C, Circle(F, radius_5_0))
- PointLiesOnCircle(D, Circle(F, ... | 117 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, A, E)), 33)",
"Equals(MeasureOf(Arc(C, B)), x)",
"Equals(MeasureOf(Arc(D, E)), 51)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnCircle(B, Circle(F, radius_5_0))",
"PointLiesOnCircle(C, Circle(F, radius_5_0))",
"PointLiesOnCircle(D, Circle... | [
"AB",
"AC",
"AD",
"AE",
"BE",
"CD",
"DE"
] | {"A": [5.0, 126.0], "B": [151.0, 138.0], "C": [183.0, 26.0], "D": [57.0, 99.0], "E": [96.0, 134.0], "F": [128.0, 71.0]} | [
"F"
] |
Diagram Logic Form:
- PointLiesOnLine(R, Line(L, M))
- PointLiesOnLine(N, Line(L, K))
- PointLiesOnLine(P, Line(M, K))
- PointLiesOnLine(Q, Line(M, N))
- PointLiesOnLine(Q, Line(R, P))
- Perpendicular(Line(K, N), Line(N, Q))
- Perpendicular(Line(M, R), Line(M, P))
If PR || KL, KN = 9, LN = 16, PM = 2 KP, find MR | 40 / 3 | [
"Parallel(Line(P,R),Line(K,L))",
"Equals(LengthOf(Line(K,N)),9)",
"Equals(LengthOf(Line(L,N)),16)",
"Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))",
"Find(LengthOf(Line(M,R)))"
] | [
"PointLiesOnLine(R, Line(L, M))",
"PointLiesOnLine(N, Line(L, K))",
"PointLiesOnLine(P, Line(M, K))",
"PointLiesOnLine(Q, Line(M, N))",
"PointLiesOnLine(Q, Line(R, P))",
"Perpendicular(Line(K, N), Line(N, Q))",
"Perpendicular(Line(M, R), Line(M, P))"
] | [
"LM",
"LK",
"LN",
"LR",
"MK",
"MN",
"MR",
"MP",
"MQ",
"KN",
"KP",
"NQ",
"RP",
"RQ",
"PQ"
] | {"L": [0.0, 0.0], "M": [249.3379381877399, 251.00262860081872], "K": [499.99869834895844, 1.331994793395836], "N": [249.99802374666012, 0.4999920949866379], "R": [83.50150150150151, 84.00150150150151], "P": [416.33335307565653, 84.99800405112472], "Q": [249.66601185756718, 84.4990000355017]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, F, C)), 70)
- Equals(MeasureOf(Angle(C, E, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, B, C)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(F, B, E)), ... | 75 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(F, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, F, C)), 70)",
"Equals(MeasureOf(Angle(C, E, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, B, C)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(F, B, E)), 35... | [
"AB",
"AD",
"AF",
"BC",
"BD",
"BE",
"BF",
"CE",
"DE",
"FC",
"FE"
] | {"A": [255.0, 2.0], "B": [39.0, 307.0], "C": [536.0, 307.0], "D": [40.0, 1.0], "E": [39.0, 172.0], "F": [119.0, 194.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, D, A)), 7y-4)
- Equals(MeasureOf(Angle(B, D, A)), 11x-1)
- Equals(MeasureOf(Angle(H, F, D)), 7x+9)
- Equals(MeasureOf(Angle(H, F, C)), z)
- Equals(MeasureOf(Angle(G, A, D)), 2y+5)
- PointLiesOnLine(F, Line(D, C))
- PointLiesOnLine(A, Line(D, E))
- Parallel(Line(A, G), Lin... | 11 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(F, D, A)), 7y-4)",
"Equals(MeasureOf(Angle(B, D, A)), 11x-1)",
"Equals(MeasureOf(Angle(H, F, D)), 7x+9)",
"Equals(MeasureOf(Angle(H, F, C)), z)",
"Equals(MeasureOf(Angle(G, A, D)), 2y+5)",
"PointLiesOnLine(F, Line(D, C))",
"PointLiesOnLine(A, Line(D, E))",
"Parallel(Line(A, G),... | [
"AD",
"AE",
"AG",
"CF",
"DB",
"DC",
"DE",
"DF",
"FH"
] | {"A": [167.0, 178.0], "B": [0.0, 41.0], "C": [277.0, 4.0], "D": [167.0, 136.0], "E": [166.0, 245.0], "F": [191.0, 107.0], "G": [1.0, 82.0], "H": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(C, B, A)), 36)
- Equals(MeasureOf(Angle(D, B, E)), 42)
- Equals(MeasureOf(Angle(B, E, D)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(D, E, C)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(E, D, B)), MeasureOf(angle ... | 53 | [
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(C, B, A)), 36)",
"Equals(MeasureOf(Angle(D, B, E)), 42)",
"Equals(MeasureOf(Angle(B, E, D)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(D, E, C)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(E, D, B)), MeasureOf(angle 7)... | [
"AB",
"AD",
"AE",
"BC",
"BD",
"BE",
"DC",
"DE",
"EC"
] | {"A": [154.0, 2.0], "B": [440.0, 1.0], "C": [0.0, 321.0], "D": [381.0, 265.0], "E": [264.0, 129.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, D, E)), 142)
- Equals(LengthOf(Line(A, E)), 3x+7)
- Equals(LengthOf(Line(B, C)), 5x-9)
- Equals(MeasureOf(Angle(B, D, C)), 142)
- PointLiesOnCircle(A, Circle(D, radius_3_0))
- PointLiesOnCircle(B, Circle(D, radius_3_0))
- PointLiesOnCircle(C, Circle(D, radius_3_0))
- Poin... | 8 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, D, E)), 142)",
"Equals(LengthOf(Line(A, E)), 3x+7)",
"Equals(LengthOf(Line(B, C)), 5x-9)",
"Equals(MeasureOf(Angle(B, D, C)), 142)",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(B, Circle(D, radius_3_0))",
"PointLiesOnCircle(C, Circle(D, radius_3_0))",
"... | [
"AE",
"BC",
"CD",
"BD",
"ED",
"AD"
] | {"A": [169.0, 8.0], "B": [57.0, 231.0], "C": [246.0, 84.0], "D": [128.0, 127.0], "E": [25.0, 200.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 18)
- Equals(LengthOf(Line(D, E)), 10)
- Equals(AreaOf(Triangle(D, E, F)), 25)
For the pair of similar figures, find the area of the green figure. | 81 | [
"Similar(Shape($1),Shape($2))",
"Find(AreaOf(Green(Shape($))))"
] | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(D, E)), 10)",
"Equals(AreaOf(Triangle(D, E, F)), 25)"
] | [
"AB",
"AC",
"BC"
] | {"A": [148.0, 144.0], "B": [0.0, 0.0], "C": [40.0, 162.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 3x-7)
- Equals(LengthOf(Line(A, B)), 2x+9)
- PointLiesOnCircle(C, Circle(P, radius_2_0))
- PointLiesOnCircle(D, Circle(P, radius_2_0))
- PointLiesOnCircle(A, Circle(O, radius_2_0))
- PointLiesOnCircle(B, Circle(O, radius_2_0))
The two circles are congruent. Find $x$. | 16 | [
"Congruent(Circle($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 3x-7)",
"Equals(LengthOf(Line(A, B)), 2x+9)",
"PointLiesOnCircle(C, Circle(P, radius_2_0))",
"PointLiesOnCircle(D, Circle(P, radius_2_0))",
"PointLiesOnCircle(A, Circle(O, radius_2_0))",
"PointLiesOnCircle(B, Circle(O, radius_2_0))"
] | [
"AB",
"CD"
] | {"A": [331.0, 264.0], "O": [178.0, 175.0], "B": [117.0, 343.0]} | [
"O",
"P"
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(D, B))
- PointLiesOnLine(E, Line(C, A))
In parallelogram $ABCD$, $\overline{BD}$ and $\overline{AC}$ intersect at $E$. If $AE = 9$, $BE = 3x - 7$, and $DE = x + 5$, find $x$. | 6 | [
"IntersectAt(Parallelogram(A,B,C,D),Line(B,D),Line(A,C),Point(E))",
"Equals(LengthOf(Line(A,E)),9)",
"Equals(LengthOf(Line(B,E)),3x-7)",
"Equals(LengthOf(Line(D,E)),x+5)",
"Find(x)"
] | [
"PointLiesOnLine(E, Line(D, B))",
"PointLiesOnLine(E, Line(C, A))"
] | [
"DB",
"DC",
"DA",
"DE",
"BC",
"BA",
"BE",
"CA",
"CE",
"AE"
] | {"D": [0.49741570010442615, 154.4984647663577], "B": [390.16201596541384, 0.0031198526269520244], "C": [321.83454574564985, 153.84513462844345], "A": [68.15788930829166, 2.1481457160496973], "E": [194.49949869661117, 77.69891718468017]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, J, H)), x)
- Equals(MeasureOf(Angle(M, H, P)), 44)
- Equals(MeasureOf(Angle(J, H, L)), 76)
- PointLiesOnLine(J, Line(K, L))
- PointLiesOnLine(P, Line(K, M))
- PointLiesOnLine(H, Line(M, L))
$\overline{JH}, \overline{JP},$ and $\overline{PH}$ are midsegments of $\triangle... | 60 | [
"IsMidsegmentOf(Line(J,H),Triangle(K,L,M))",
"IsMidsegmentOf(Line(J,P),Triangle(K,L,M))",
"IsMidsegmentOf(Line(P,H),Triangle(K,L,M))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(L, J, H)), x)",
"Equals(MeasureOf(Angle(M, H, P)), 44)",
"Equals(MeasureOf(Angle(J, H, L)), 76)",
"PointLiesOnLine(J, Line(K, L))",
"PointLiesOnLine(P, Line(K, M))",
"PointLiesOnLine(H, Line(M, L))"
] | [
"PH",
"PJ",
"PK",
"PM",
"HJ",
"HL",
"HM",
"JL",
"JK",
"KL",
"KM",
"ML"
] | {"P": [35.1807617820904, 130.78330096394896], "H": [169.84726105815162, 260.63752221963443], "J": [201.10682312965855, 128.641594867987], "L": [338.0, 260.0], "K": [67.13362386099949, 1.1113060539174455], "M": [0.8374204753544348, 259.66815804874363]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, E)), x)
- Equals(LengthOf(Line(E, C)), x+3)
- Equals(LengthOf(Line(D, E)), x+10)
- Equals(LengthOf(Line(E, A)), x+1)
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(E, Line(C, A))
- PointLiesOnCircle(B, Circle(F, radius_1_0))
- PointLiesOnCircle(C, Circle(F, radius_1_0))... | 0.5 | [
"Find(MeasureOf(x))"
] | [
"Equals(LengthOf(Line(B, E)), x)",
"Equals(LengthOf(Line(E, C)), x+3)",
"Equals(LengthOf(Line(D, E)), x+10)",
"Equals(LengthOf(Line(E, A)), x+1)",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnCircle(B, Circle(F, radius_1_0))",
"PointLiesOnCircle(C, Circle(F, radius_1... | [
"BD",
"BE",
"BF",
"CA",
"DE",
"EA",
"EC",
"FD",
"FE"
] | {"A": [2.0, 115.0], "B": [48.0, 15.0], "C": [148.0, 19.0], "D": [146.0, 177.0], "E": [78.0, 65.0], "F": [95.0, 99.0]} | [
"F"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, G, B)), MeasureOf(Angle(19)))
- Equals(MeasureOf(Angle(B, G, D)), MeasureOf(Angle(20)))
- PointLiesOnLine(G, Line(B, E))
- PointLiesOnLine(G, Line(C, D))
$m∠19 = 100 + 20x$, $m∠20 = 20x $. Find the measure of $\angle 19$. | 140 | [
"Equals(MeasureOf(Angle(19)),100+20x)",
"Equals(MeasureOf(Angle(20)),20x)",
"Find(MeasureOf(Angle(19)))"
] | [
"Equals(MeasureOf(Angle(C, G, B)), MeasureOf(Angle(19)))",
"Equals(MeasureOf(Angle(B, G, D)), MeasureOf(Angle(20)))",
"PointLiesOnLine(G, Line(B, E))",
"PointLiesOnLine(G, Line(C, D))"
] | [
"BE",
"BG",
"CD",
"EG",
"GC",
"GD"
] | {"B": [7.0, 110.0], "C": [35.0, 3.0], "D": [206.0, 179.0], "E": [242.0, 96.0], "G": [131.0, 102.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 21)
- Equals(LengthOf(Line(C, B)), 15)
- Equals(LengthOf(Line(C, A)), 16)
- Perpendicular(Line(C, B), Line(C, A))
find cos B | \frac { 5 } { 7 } | [
"Find(CosOf(Angle(B)))"
] | [
"Equals(LengthOf(Line(A, B)), 21)",
"Equals(LengthOf(Line(C, B)), 15)",
"Equals(LengthOf(Line(C, A)), 16)",
"Perpendicular(Line(C, B), Line(C, A))"
] | [
"CA",
"CB",
"AB"
] | {"C": [154.02029985405335, 144.01884038742207], "A": [1.4210854715202004e-14, 146.0], "B": [156.0, 1.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, T)), 13)
- Equals(LengthOf(Line(X, Y)), 7)
- Equals(MeasureOf(Angle(Z, X, Y)), 124)
- PointLiesOnLine(Y, Line(R, T))
- PointLiesOnLine(X, Line(R, S))
- PointLiesOnLine(Z, Line(T, S))
$\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $XZ$. | 6.5 | [
"IsMidsegmentOf(Line(X,Y),Triangle(R,S,T))",
"IsMidsegmentOf(Line(X,Z),Triangle(R,S,T))",
"Find(LengthOf(Line(X,Z)))"
] | [
"Equals(LengthOf(Line(R, T)), 13)",
"Equals(LengthOf(Line(X, Y)), 7)",
"Equals(MeasureOf(Angle(Z, X, Y)), 124)",
"PointLiesOnLine(Y, Line(R, T))",
"PointLiesOnLine(X, Line(R, S))",
"PointLiesOnLine(Z, Line(T, S))"
] | [
"RS",
"RT",
"RX",
"RY",
"SX",
"SZ",
"TS",
"TY",
"TZ",
"XY",
"XZ"
] | {"R": [1.0, 325.0], "S": [535.0, 1.0], "T": [385.0, 326.0], "X": [273.0, 160.0], "Y": [158.0, 325.0], "Z": [461.0, 162.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, X, V)), 2x+65)
- Equals(MeasureOf(Angle(Y, X, W)), 4x+15)
- PointLiesOnLine(X, Line(W, Z))
- PointLiesOnLine(X, Line(Y, V))
- PointLiesOnCircle(W, Circle(X, radius_1_0))
- PointLiesOnCircle(Y, Circle(X, radius_1_0))
- PointLiesOnCircle(V, Circle(X, radius_1_0))
- PointLie... | 65 | [
"Find(MeasureOf(Angle(Z,X,Y)))"
] | [
"Equals(MeasureOf(Angle(Z, X, V)), 2x+65)",
"Equals(MeasureOf(Angle(Y, X, W)), 4x+15)",
"PointLiesOnLine(X, Line(W, Z))",
"PointLiesOnLine(X, Line(Y, V))",
"PointLiesOnCircle(W, Circle(X, radius_1_0))",
"PointLiesOnCircle(Y, Circle(X, radius_1_0))",
"PointLiesOnCircle(V, Circle(X, radius_1_0))",
"Poin... | [
"XV",
"XW",
"XY",
"XZ",
"YV",
"ZW"
] | {"V": [177.0, 56.0], "W": [158.0, 141.0], "X": [96.0, 84.0], "Y": [20.0, 115.0], "Z": [35.0, 28.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, C, D)), 66)
- Equals(MeasureOf(Angle(C, D, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, D, B)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(D, A, C)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(D, B, A)), 24)
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle ... | 66 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(A, C, D)), 66)",
"Equals(MeasureOf(Angle(C, D, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, D, B)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(D, A, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(D, B, A)), 24)",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2)... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [600.9234345586568, 270.49808450019486], "B": [2.2132352941176237, 269.00735294117646], "C": [601.998767948655, 0.6672192478346801], "D": [363.5242226421577, 107.36122904753725]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 5)
- Equals(LengthOf(Line(C, D)), 4)
- Equals(LengthOf(Line(B, D)), 3)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(A, C), Line(C, B))
- Perpendicular(Line(C, D), Line(A, D))
Find the perimeter of the given triangle. $\triangle A B C,$ if $\triangle A B C \si... | 20 | [
"Triangle(A,B,C)",
"Similar(Triangle(A,B,C),Triangle(C,B,D))",
"Equals(LengthOf(Line(C,D)),4)",
"Equals(LengthOf(Line(D,B)),3)",
"Equals(LengthOf(Line(C,B)),5)",
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(C, B)), 5)",
"Equals(LengthOf(Line(C, D)), 4)",
"Equals(LengthOf(Line(B, D)), 3)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(A, C), Line(C, B))",
"Perpendicular(Line(C, D), Line(A, D))"
] | [
"AB",
"AC",
"AD",
"BD",
"CB",
"CD"
] | {"A": [0.0, 148.0], "B": [308.0, 148.0], "C": [198.0, 0.0], "D": [196.0, 148.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 27)
- Equals(LengthOf(Line(C, H)), 7)
- Equals(MeasureOf(Angle(A, B, C)), 135)
- PointLiesOnLine(I, Line(A, D))
- PointLiesOnLine(I, Line(A, H))
- PointLiesOnLine(H, Line(I, D))
- PointLiesOnLine(H, Line(A, D))
- Perpendicular(Line(I, F), Line(B, I))
- Perpendicular(Li... | 40 + 14 \sqrt { 2 } | [
"Find(PerimeterOf(Quadrilateral(A,B,C,D)))"
] | [
"Equals(LengthOf(Line(A, D)), 27)",
"Equals(LengthOf(Line(C, H)), 7)",
"Equals(MeasureOf(Angle(A, B, C)), 135)",
"PointLiesOnLine(I, Line(A, D))",
"PointLiesOnLine(I, Line(A, H))",
"PointLiesOnLine(H, Line(I, D))",
"PointLiesOnLine(H, Line(A, D))",
"Perpendicular(Line(I, F), Line(B, I))",
"Perpendic... | [
"AB",
"BC",
"CD",
"AD",
"AI",
"IH",
"HD",
"AH",
"ID",
"BI",
"CH"
] | {"A": [1.0, 8.0], "B": [135.0, 139.0], "C": [386.0, 140.0], "D": [513.0, 8.0], "H": [384.0, 8.0], "I": [132.0, 8.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, C)), 55)
- Equals(LengthOf(Line(E, C)), x+4)
- Equals(MeasureOf(Angle(D, A, E)), 60)
- Equals(MeasureOf(Angle(C, B, A)), 5y)
- Equals(LengthOf(Line(E, D)), 3x-6)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(E, Line(C, D))
Find $y$ so that the quadrilateral is a ... | 12 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(B, A, C)), 55)",
"Equals(LengthOf(Line(E, C)), x+4)",
"Equals(MeasureOf(Angle(D, A, E)), 60)",
"Equals(MeasureOf(Angle(C, B, A)), 5y)",
"Equals(LengthOf(Line(E, D)), 3x-6)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(E, Line(C, D))"
] | [
"AB",
"AC",
"AD",
"AE",
"BC",
"BD",
"BE",
"CD",
"CE",
"DE"
] | {"A": [346.0, 2.0], "B": [127.0, 190.0], "C": [0.0, 0.0], "D": [473.0, 192.0], "E": [237.0, 96.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(V, B)), 8)
- Equals(LengthOf(Line(H, J)), 9)
- Equals(LengthOf(Line(G, J)), 6)
- Equals(LengthOf(Line(B, C)), x)
- PointLiesOnLine(C, Line(A, V))
- PointLiesOnLine(I, Line(G, H))
- Perpendicular(Line(B, C), Line(V, C))
- Perpendicular(Line(G, H), Line(H, J))
- Equals(MeasureOf... | 12 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(V, B)), 8)",
"Equals(LengthOf(Line(H, J)), 9)",
"Equals(LengthOf(Line(G, J)), 6)",
"Equals(LengthOf(Line(B, C)), x)",
"PointLiesOnLine(C, Line(A, V))",
"PointLiesOnLine(I, Line(G, H))",
"Perpendicular(Line(B, C), Line(V, C))",
"Perpendicular(Line(G, H), Line(H, J))",
"Equals(Me... | [
"AB",
"AC",
"AV",
"BC",
"VB",
"VC",
"GH",
"GI",
"HI",
"GJ",
"HJ",
"IJ"
] | {"A": [0.0, 232.0], "B": [185.0, 2.0], "C": [186.0, 232.0], "V": [416.0, 231.0], "G": [410.0, 2.0], "H": [600.0, 2.0], "I": [750.0, 2.0], "J": [600.0, 200.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, D)), x-4)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(E, F)), 3)
- Equals(LengthOf(Line(C, B)), 5)
- Equals(MeasureOf(Angle(B, A, C)), MeasureOf(Angle(E, D, F)))
- Equals(MeasureOf(Angle(C, B, A)), MeasureOf(Angle(D, E, F)))
Find DE | 6 | [
"Find(LengthOf(Line(D,E)))"
] | [
"Equals(LengthOf(Line(E, D)), x-4)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(E, F)), 3)",
"Equals(LengthOf(Line(C, B)), 5)",
"Equals(MeasureOf(Angle(B, A, C)), MeasureOf(Angle(E, D, F)))",
"Equals(MeasureOf(Angle(C, B, A)), MeasureOf(Angle(D, E, F)))"
] | [
"AB",
"AC",
"CB",
"ED",
"EF",
"FD"
] | {"A": [72.0, 6.0], "B": [2.0, 158.0], "C": [138.0, 157.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, P)), 2x)
- Equals(LengthOf(Line(Q, R)), 3y+8)
- Equals(LengthOf(Line(S, R)), 2y)
- Equals(LengthOf(Line(S, P)), x)
- PointLiesOnLine(S, Line(R, P))
- Perpendicular(Line(Q, S), Line(S, R))
$\triangle PQS \cong \triangle RQS$. Find $x$. | 16 | [
"Congruent(Triangle(P,Q,S),Triangle(R,Q,S))",
"Find(x)"
] | [
"Equals(LengthOf(Line(Q, P)), 2x)",
"Equals(LengthOf(Line(Q, R)), 3y+8)",
"Equals(LengthOf(Line(S, R)), 2y)",
"Equals(LengthOf(Line(S, P)), x)",
"PointLiesOnLine(S, Line(R, P))",
"Perpendicular(Line(Q, S), Line(S, R))"
] | [
"QP",
"QR",
"QS",
"RP",
"SP",
"SR"
] | {"P": [1.0, 322.0], "Q": [338.0, 1.0], "R": [674.0, 322.0], "S": [336.0, 322.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, G)), 10)
- Equals(LengthOf(Line(E, G)), 10)
- PointLiesOnLine(E, Line(D, F))
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnCircle(D, Circle(G, radius_2_0))
- PointLiesOnCircle(A, Circle(G, radius_2_0))
- PointLiesOnCircle(F, Circle(G, radius_2_0))
- PointLiesOnCircle(C, Cir... | 24 | [
"IsChordOf(Line(A,C),Circle($))",
"IsChordOf(Line(D,F),Circle($))",
"Line(A,C)",
"Line(D,F)",
"Equals(RadiusOf(Circle(G)),26)",
"Find(LengthOf(Line(D,E)))"
] | [
"Equals(LengthOf(Line(B, G)), 10)",
"Equals(LengthOf(Line(E, G)), 10)",
"PointLiesOnLine(E, Line(D, F))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnCircle(D, Circle(G, radius_2_0))",
"PointLiesOnCircle(A, Circle(G, radius_2_0))",
"PointLiesOnCircle(F, Circle(G, radius_2_0))",
"PointLiesOnCircle(C,... | [
"AB",
"AC",
"AG",
"BG",
"CB",
"DE",
"DF",
"EG",
"FE",
"FG"
] | {"A": [85.0, 1.0], "B": [132.0, 52.0], "C": [177.0, 102.0], "D": [64.0, 174.0], "E": [36.0, 111.0], "F": [10.0, 48.0], "G": [89.0, 88.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, E, C)), 9x-1)
- Equals(MeasureOf(Angle(D, E, C)), 94)
- Equals(MeasureOf(Angle(D, B, C)), 2x)
- PointLiesOnLine(D, Line(A, B))
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnCircle(A, Circle(E, radius_4_0))
- PointLiesOnCircle(C, Circle(E, radius_4_0))
- PointLiesOnCircle(... | 19 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, E, C)), 9x-1)",
"Equals(MeasureOf(Angle(D, E, C)), 94)",
"Equals(MeasureOf(Angle(D, B, C)), 2x)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnCircle(A, Circle(E, radius_4_0))",
"PointLiesOnCircle(C, Circle(E, radius_4_0))",
"PointLiesOnCir... | [
"",
"AB",
"AD",
"BC",
"BD"
] | {"A": [220.0, 3.0], "B": [1.0, 247.0], "C": [250.0, 248.0], "D": [116.0, 119.0], "E": [239.0, 127.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 15)
- Equals(LengthOf(Line(D, E)), 10)
- Equals(MeasureOf(Angle(D, E, C)), 60)
Find the area of the figure. Round to the nearest tenth. | 129.9 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, D)), 15)",
"Equals(LengthOf(Line(D, E)), 10)",
"Equals(MeasureOf(Angle(D, E, C)), 60)"
] | [
"AC",
"AD",
"BF",
"CE",
"DE"
] | {"A": [295.0, 1.0], "B": [74.0, 105.0], "C": [224.0, 130.0], "D": [74.0, 1.0], "E": [1.0, 129.0], "F": [96.0, 112.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), LengthOf(h))
- Equals(LengthOf(Line(A, C)), 15)
- Equals(MeasureOf(Angle(A, C, B)), 60)
- Perpendicular(Line(A, B), Line(A, C))
Find $h$. | 15 \sqrt 3 | [
"Find(h)"
] | [
"Equals(LengthOf(Line(A, B)), LengthOf(h))",
"Equals(LengthOf(Line(A, C)), 15)",
"Equals(MeasureOf(Angle(A, C, B)), 60)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [67.44146927566084, 0.7274287675935511], "B": [277.0, 119.0], "C": [0.1900840624463882, 118.33401955738549]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(2)), MeasureOf(Angle(E, A, C)))
- Equals(MeasureOf(Arc(E, A)), 100)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLine(E, Line(A, F))
- PointLiesOnLine(F, Line(B, E))
- PointLiesOnCircle(A, Circle(D, radius_3_... | 130 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(2)), MeasureOf(Angle(E, A, C)))",
"Equals(MeasureOf(Arc(E, A)), 100)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(G, Line(A, C))",
"PointLiesOnLine(E, Line(A, F))",
"PointLiesOnLine(F, Line(B, E))",
"PointLiesOnCircle(A, Circle(D, radiu... | [
"AB",
"AC",
"AE",
"AF",
"AG",
"BE",
"BF",
"CG",
"EF"
] | {"A": [123.0, 109.0], "B": [2.0, 10.0], "C": [221.0, 81.0], "D": [114.0, 56.0], "E": [59.0, 57.0], "F": [18.0, 22.0], "G": [141.0, 102.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, M)), 6)
- PointLiesOnLine(M, Line(K, A))
- PointLiesOnLine(M, Line(L, J))
- PointLiesOnLine(K, Line(M, C))
- PointLiesOnLine(K, Line(A, C))
- PointLiesOnLine(M, Line(A, C))
- Perpendicular(Line(L, M), Line(K, M))
- Equals(LengthOf(Line(K, J)), LengthOf(Line(K, L)))
Find $J... | 12 | [
"Find(LengthOf(Line(J,L)))"
] | [
"Equals(LengthOf(Line(J, M)), 6)",
"PointLiesOnLine(M, Line(K, A))",
"PointLiesOnLine(M, Line(L, J))",
"PointLiesOnLine(K, Line(M, C))",
"PointLiesOnLine(K, Line(A, C))",
"PointLiesOnLine(M, Line(A, C))",
"Perpendicular(Line(L, M), Line(K, M))",
"Equals(LengthOf(Line(K, J)), LengthOf(Line(K, L)))"
] | [
"AC",
"BC",
"JM",
"KA",
"KB",
"KC",
"KJ",
"KL",
"KM",
"LB",
"LJ",
"LM",
"MA",
"MC"
] | {"A": [142.0, 0.0], "B": [235.0, 133.0], "C": [143.0, 296.0], "J": [-0.0, 56.0], "K": [143.0, 276.0], "L": [290.0, 58.0], "M": [142.0, 57.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, U)), 15\sqrt{3})
- Equals(MeasureOf(Angle(S, U, T)), 63)
- Equals(LengthOf(Line(S, U)), x)
- Perpendicular(Line(T, U), Line(T, S))
Find x. Round to the nearest tenth. | 57.2 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(T, U)), 15\\sqrt{3})",
"Equals(MeasureOf(Angle(S, U, T)), 63)",
"Equals(LengthOf(Line(S, U)), x)",
"Perpendicular(Line(T, U), Line(T, S))"
] | [
"SU",
"TS",
"TU"
] | {"S": [1.0, 218.0], "T": [2.0, 0.0], "U": [110.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, T, W)), MeasureOf(Angle(Y, W, T)))
- Equals(MeasureOf(Angle(T, Z, Y)), MeasureOf(Angle(Z, Y, W)))
isosceles trapezoid TWYZ with $\angle Z \cong \angle Y, m \angle Z=30 x$, $\angle T \cong \angle W,$ and $m \angle T=20 x$, find $\angle W$ | 72 | [
"Isosceles(Trapezoid(T,W,Y,Z))",
"Equals(Angle(Z),Angle(Y))",
"Equals(MeasureOf(Angle(Z)),30x)",
"Equals(Angle(T),Angle(W))",
"Equals(MeasureOf(Angle(T)),20x)",
"Find(MeasureOf(Angle(T)))"
] | [
"Equals(MeasureOf(Angle(Z, T, W)), MeasureOf(Angle(Y, W, T)))",
"Equals(MeasureOf(Angle(T, Z, Y)), MeasureOf(Angle(Z, Y, W)))"
] | [
"WT",
"YW",
"YZ",
"ZT"
] | {"T": [1.0, 2.0], "W": [249.0, 0.0], "Y": [212.0, 108.0], "Z": [37.0, 107.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 24)
- Equals(LengthOf(Line(C, B)), 10)
- Equals(LengthOf(Line(A, B)), 26)
- Perpendicular(Line(A, C), Line(C, B))
Express the ratio of $\tan B$ as a decimal to the nearest hundredth. | 2.40 | [
"Find(RatioOf(TanOf(Angle(B))))"
] | [
"Equals(LengthOf(Line(A, C)), 24)",
"Equals(LengthOf(Line(C, B)), 10)",
"Equals(LengthOf(Line(A, B)), 26)",
"Perpendicular(Line(A, C), Line(C, B))"
] | [
"AC",
"AB",
"CB"
] | {"A": [2.842170943040401e-14, 128.0], "C": [301.8951128955662, 0.8503432197901901], "B": [358.0, 129.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 20)
- Equals(LengthOf(Line(D, B)), 2x+1)
- Equals(MeasureOf(Angle(A, C, B)), 22)
- Equals(MeasureOf(Angle(C, B, D)), 22)
- Equals(LengthOf(Line(C, F)), 12)
- Equals(LengthOf(Line(F, B)), 2x-1)
- PointLiesOnLine(D, Line(A, F))
- PointLiesOnLine(F, Line(C, B))
- Perpendi... | 15 | [
"Find(LengthOf(Line(C,B)))"
] | [
"Equals(LengthOf(Line(A, C)), 20)",
"Equals(LengthOf(Line(D, B)), 2x+1)",
"Equals(MeasureOf(Angle(A, C, B)), 22)",
"Equals(MeasureOf(Angle(C, B, D)), 22)",
"Equals(LengthOf(Line(C, F)), 12)",
"Equals(LengthOf(Line(F, B)), 2x-1)",
"PointLiesOnLine(D, Line(A, F))",
"PointLiesOnLine(F, Line(C, B))",
"P... | [
"AC",
"AF",
"AD",
"CB",
"CF",
"FB",
"FD",
"DB"
] | {"A": [258.0025258458647, 1.3307291666666856], "C": [0.32330827067667656, 266.33333333333337], "B": [442.6769759450172, 266.33333333333337], "F": [256.0075187969925, 267.0], "D": [256.22358917374396, 74.26263989205492]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), z)
- Equals(LengthOf(Line(A, D)), y)
- Equals(LengthOf(Line(B, D)), 6)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(C, D)), 4)
- PointLiesOnLine(D, Line(B, C))
- Perpendicular(Line(A, B), Line(A, C))
- Perpendicular(Line(A, D), Line(B, D))
Find x. | 2 \sqrt { 10 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), z)",
"Equals(LengthOf(Line(A, D)), y)",
"Equals(LengthOf(Line(B, D)), 6)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(C, D)), 4)",
"PointLiesOnLine(D, Line(B, C))",
"Perpendicular(Line(A, B), Line(A, C))",
"Perpendicular(Line(A, D), Line(B, D))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [1.4509174609349742, 0.7325130684195216], "B": [274.4683760683761, 0.33162393162393045], "C": [1.3333333333333286, 196.85644768856446], "D": [93.70788219208455, 130.58852222755996]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Y, Z, I)), 20)
- Equals(MeasureOf(Angle(W, X, J)), 130)
- PointLiesOnLine(H, Line(G, I))
- PointLiesOnLine(H, Line(G, Z))
- PointLiesOnLine(I, Line(H, Z))
- PointLiesOnLine(I, Line(G, Z))
- PointLiesOnLine(H, Line(J, X))
- PointLiesOnLine(I, Line(J, Y))
- PointLiesOnLine(X, ... | 110 | [
"Equals(RatioOf(Line(I,J),Line(X,J)),RatioOf(Line(H,J),Line(Y,J)))",
"Equals(MeasureOf(Angle(W,X,J)),130)",
"Equals(MeasureOf(Angle(W,Z,G)),20)",
"Find(MeasureOf(Angle(J,H,G)))"
] | [
"Equals(MeasureOf(Angle(Y, Z, I)), 20)",
"Equals(MeasureOf(Angle(W, X, J)), 130)",
"PointLiesOnLine(H, Line(G, I))",
"PointLiesOnLine(H, Line(G, Z))",
"PointLiesOnLine(I, Line(H, Z))",
"PointLiesOnLine(I, Line(G, Z))",
"PointLiesOnLine(H, Line(J, X))",
"PointLiesOnLine(I, Line(J, Y))",
"PointLiesOnL... | [
"GH",
"GI",
"GZ",
"HI",
"HX",
"HZ",
"IY",
"IZ",
"JH",
"JI",
"JX",
"JY",
"WX",
"WY",
"WZ",
"XY",
"XZ",
"YZ"
] | {"C": [544.0, 199.0], "D": [0.0, 199.0], "G": [198.0, 103.0], "H": [235.0, 116.0], "I": [401.0, 186.0], "J": [331.0, 2.0], "W": [78.0, 202.0], "X": [163.0, 200.0], "Z": [455.0, 199.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(B, D))
- PointLiesOnLine(P, Line(A, C))
- Perpendicular(Line(A, P), Line(D, P))
Quadrilateral $ABCD$ is a rhombus. If $m\angle BCD = 54$, find $m\angle BAC$. | 27 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(B,C,D)),54)",
"Find(MeasureOf(Angle(B,A,C)))"
] | [
"PointLiesOnLine(P, Line(B, D))",
"PointLiesOnLine(P, Line(A, C))",
"Perpendicular(Line(A, P), Line(D, P))"
] | [
"BD",
"BA",
"BC",
"BP",
"DA",
"DC",
"DP",
"AC",
"AP",
"CP"
] | {"B": [220.5954165289054, 1.662674650698591], "D": [0.0, 163.0], "A": [54.84151329243353, 1.5], "C": [166.77464155029716, 161.84853144795147], "P": [111.0, 81.5]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 4w-7)
- Equals(LengthOf(Line(U, T)), z+16)
- Equals(MeasureOf(Angle(E, B, C)), 2x+9)
- Equals(MeasureOf(Angle(U, T, S)), y+11)
- Equals(LengthOf(Line(R, U)), 12)
- Equals(LengthOf(Line(C, D)), 11)
- Equals(MeasureOf(Angle(E, D, C)), 2y-31)
- Equals(MeasureOf(Angle(S, R... | 42 | [
"Congruent(Quadrilateral(B,C,D,E),Quadrilateral(R,S,T,U))",
"Find(y)"
] | [
"Equals(LengthOf(Line(C, B)), 4w-7)",
"Equals(LengthOf(Line(U, T)), z+16)",
"Equals(MeasureOf(Angle(E, B, C)), 2x+9)",
"Equals(MeasureOf(Angle(U, T, S)), y+11)",
"Equals(LengthOf(Line(R, U)), 12)",
"Equals(LengthOf(Line(C, D)), 11)",
"Equals(MeasureOf(Angle(E, D, C)), 2y-31)",
"Equals(MeasureOf(Angle(... | [
"CB",
"DC",
"DE",
"EB",
"RU",
"SR",
"TS",
"UT"
] | {"B": [0.0, 0.0], "C": [677.0, 0.0], "D": [437.0, 275.0], "E": [239.0, 274.0], "R": [800.0, 274.0], "S": [1477.0, 274.0], "T": [1200.0, 0.0], "U": [1000.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 10)
- Equals(LengthOf(Line(N, B)), 7)
- Equals(LengthOf(Line(N, C)), 12.2)
- PointLiesOnLine(E, Line(B, N))
- Perpendicular(Line(A, E), Line(E, N))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 70 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(A, E)), 10)",
"Equals(LengthOf(Line(N, B)), 7)",
"Equals(LengthOf(Line(N, C)), 12.2)",
"PointLiesOnLine(E, Line(B, N))",
"Perpendicular(Line(A, E), Line(E, N))"
] | [
"AB",
"AC",
"BN",
"CN"
] | {"A": [38.0, 0.0], "B": [0.0, 131.0], "C": [142.0, 1.0], "N": [107.0, 132.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, G, H)), 3x+6)
- Perpendicular(Line(E, H), Line(H, G))
- Equals(LengthOf(Line(E, H)), LengthOf(Line(H, G)))
Find $x$. | 13 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, G, H)), 3x+6)",
"Perpendicular(Line(E, H), Line(H, G))",
"Equals(LengthOf(Line(E, H)), LengthOf(Line(H, G)))"
] | [
"EH",
"GE",
"GH"
] | {"E": [1.0, 1.0], "G": [356.0, 36.0], "H": [163.0, 196.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 53 | [
"Equals(MeasureOf(Angle(1)),53)",
"Find(MeasureOf(Angle(6)))"
] | [
"Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"GN",
"GW",
"GX",
"HE",
"HZ",
"HZ",
"IK",
"IY",
"IZ",
"ML",
"MW",
"MY",
"WL",
"WN",
"WX",
"XE",
"XN",
"YK",
"YL",
"YW",
"YZ",
"ZE",
"ZK",
"ZX"
] | {"E": [331.0, 74.0], "G": [57.0, 80.0], "H": [165.0, 365.0], "I": [1.0, 198.0], "K": [295.0, 360.0], "L": [184.0, 6.0], "M": [23.0, 289.0], "N": [358.0, 248.0], "W": [122.0, 116.0], "X": [261.0, 194.0], "Y": [58.0, 228.0], "Z": [199.0, 305.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, B)), 3x+25)
- Equals(MeasureOf(Angle(C, D, B)), 4x+5)
- Equals(MeasureOf(Angle(D, B, C)), 5x-30)
Solve for $x$. | 15 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, C, B)), 3x+25)",
"Equals(MeasureOf(Angle(C, D, B)), 4x+5)",
"Equals(MeasureOf(Angle(D, B, C)), 5x-30)"
] | [
"CB",
"CD",
"DB"
] | {"B": [549.0, 372.0], "C": [451.0, 0.0], "D": [0.0, 371.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, E, D)), 2x+10)
- Equals(MeasureOf(Angle(C, D, E)), x)
- Equals(MeasureOf(Angle(B, C, D)), 2x-20)
- PointLiesOnLine(F, Line(A, E))
- Perpendicular(Line(F, A), Line(A, B))
- Perpendicular(Line(A, B), Line(C, B))
Find $m\angle C$ | 128 | [
"Find(MeasureOf(Angle(C)))"
] | [
"Equals(MeasureOf(Angle(A, E, D)), 2x+10)",
"Equals(MeasureOf(Angle(C, D, E)), x)",
"Equals(MeasureOf(Angle(B, C, D)), 2x-20)",
"PointLiesOnLine(F, Line(A, E))",
"Perpendicular(Line(F, A), Line(A, B))",
"Perpendicular(Line(A, B), Line(C, B))"
] | [
"AB",
"AE",
"CB",
"DC",
"ED",
"FA",
"FE"
] | {"A": [1.0, 1.0], "B": [2.0, 208.0], "C": [210.0, 206.0], "D": [334.0, 80.0], "E": [211.0, 2.0], "F": [122.0, 3.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 4)
- Equals(LengthOf(Line(A, B)), 6)
- Equals(LengthOf(Line(C, D)), x)
- Equals(LengthOf(Line(B, C)), x+3)
- PointLiesOnLine(D, Line(A, C))
- Equals(MeasureOf(Angle(D, B, A)), MeasureOf(Angle(D, B, C)))
-
Find x | 6 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 4)",
"Equals(LengthOf(Line(A, B)), 6)",
"Equals(LengthOf(Line(C, D)), x)",
"Equals(LengthOf(Line(B, C)), x+3)",
"PointLiesOnLine(D, Line(A, C))",
"Equals(MeasureOf(Angle(D, B, A)), MeasureOf(Angle(D, B, C)))",
""
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [227.0, 1.0], "B": [239.0, 179.0], "C": [0.0, 199.0], "D": [135.0, 81.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, B, C)), 18)
- Equals(LengthOf(Line(D, B)), 12)
Find the perimeter of the triangle. Round to the nearest hundredth. | 28.52 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(MeasureOf(Angle(D, B, C)), 18)",
"Equals(LengthOf(Line(D, B)), 12)"
] | [
"BC",
"DB",
"DC"
] | {"B": [252.0, 2.0], "C": [1.0, 47.0], "D": [38.0, 119.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))
- PointLiesOnLine(A, Line(J, G))
- PointLiesOnLine(B, Line(J, G))
- PointLiesOnLine(A, Line(J, B))
- PointLiesOnLine(B, Line(H, F))
... | 39 | [
"Equals(MeasureOf(Arc(G,H)),78)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(H, G, A)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, H, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, J, H)), MeasureOf(angle 3))",
"PointLiesOnLine(A, Line(J, G))",
"PointLiesOnLine(B, Line(J, G))",
"PointLiesOnLine(A, Line(J, B))",
"PointLiesOnLine(B, Line(H, F))... | [
"AB",
"BF",
"GA",
"GB",
"HB",
"HF",
"HG",
"JA",
"JB",
"JG",
"JH"
] | {"A": [105.0, 106.0], "B": [102.0, 82.0], "F": [4.0, 80.0], "G": [100.0, 2.0], "H": [202.0, 83.0], "J": [103.0, 205.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(X, Z))
- PointLiesOnLine(A, Line(W, Y))
- Perpendicular(Line(X, W), Line(W, Z))
Quadrilateral WXYZ is a rectangle. If $XW = 3$, $WZ = 4$, and $XZ = b$, find $YW$. | 5 | [
"Rectangle(W,X,Y,Z)",
"Equals(LengthOf(Line(X,W)),3)",
"Equals(LengthOf(Line(W,Z)),4)",
"Equals(LengthOf(Line(X,Z)),b)",
"Find(LengthOf(Line(Y,W)))"
] | [
"PointLiesOnLine(A, Line(X, Z))",
"PointLiesOnLine(A, Line(W, Y))",
"Perpendicular(Line(X, W), Line(W, Z))"
] | [
"WA",
"WY",
"XA",
"XW",
"XY",
"XZ",
"YA",
"ZA",
"ZW",
"ZY"
] | {"A": [140.0, 47.0], "W": [1.0, 93.0], "X": [1.0, 1.0], "Y": [276.0, 2.0], "Z": [277.0, 92.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, B)), 80)
- Equals(LengthOf(Line(A, B)), 4y-2)
- Equals(LengthOf(Line(A, C)), 2y+2)
- Equals(MeasureOf(Angle(B, C, A)), 6x+8)
- Equals(LengthOf(Line(A, B)), LengthOf(Line(A, C)))
Find $y$. | 2 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(C, A, B)), 80)",
"Equals(LengthOf(Line(A, B)), 4y-2)",
"Equals(LengthOf(Line(A, C)), 2y+2)",
"Equals(MeasureOf(Angle(B, C, A)), 6x+8)",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(A, C)))"
] | [
"AB",
"AC",
"BC"
] | {"A": [221.49172576832152, 0.19858156028368512], "B": [0.5848597220661702, 250.6694385136907], "C": [422.0, 252.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, M)), 20)
- Equals(LengthOf(Line(L, K)), z)
- Equals(LengthOf(Line(L, M)), x)
- Equals(LengthOf(Line(J, M)), 5)
- Equals(LengthOf(Line(L, J)), y)
- PointLiesOnLine(M, Line(K, J))
- Perpendicular(Line(K, M), Line(L, M))
- Perpendicular(Line(L, K), Line(L, J))
Find $z$. | 10 \sqrt { 5 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(K, M)), 20)",
"Equals(LengthOf(Line(L, K)), z)",
"Equals(LengthOf(Line(L, M)), x)",
"Equals(LengthOf(Line(J, M)), 5)",
"Equals(LengthOf(Line(L, J)), y)",
"PointLiesOnLine(M, Line(K, J))",
"Perpendicular(Line(K, M), Line(L, M))",
"Perpendicular(Line(L, K), Line(L, J))"
] | [
"JM",
"KJ",
"KM",
"LJ",
"LK",
"LM"
] | {"J": [0.0, 346.0], "K": [173.0, 0.0], "L": [173.0, 347.0], "M": [33.0, 279.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(C, B, A)), 17)
- Equals(MeasureOf(Angle(C, E, A)), 29)
- PointLiesOnLine(E, Line(B, C))
- PointLiesOnLine(C... | 151 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(E, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(B, A, E)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, E, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(C, B, A)), 17)",
"Equals(MeasureOf(Angle(C, E, A)), 29)",
"PointLiesOnLine(E, Line(B, C))",
"PointLiesOnLine(... | [
"AB",
"AD",
"AE",
"BC",
"BD",
"BE",
"DC",
"DE",
"EC"
] | {"A": [3.0, 0.0], "B": [684.0, 209.0], "C": [288.0, 209.0], "D": [0.0, 209.0], "E": [371.0, 210.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, E)), x+6)
- Equals(LengthOf(Line(A, E)), 10)
- Equals(LengthOf(Line(B, E)), 11)
- Equals(LengthOf(Line(C, B)), y-7)
- PointLiesOnLine(E, Line(C, A))
- PointLiesOnLine(E, Line(D, B))
Use parallelogram to find $y$ | 17 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(D, E)), x+6)",
"Equals(LengthOf(Line(A, E)), 10)",
"Equals(LengthOf(Line(B, E)), 11)",
"Equals(LengthOf(Line(C, B)), y-7)",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnLine(E, Line(D, B))"
] | [
"AB",
"AD",
"AE",
"BE",
"CA",
"CB",
"CD",
"CE",
"DB",
"DE"
] | {"A": [3.0, 2.0], "B": [81.0, 222.0], "C": [390.0, 256.0], "D": [312.0, 38.0], "E": [198.0, 130.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, J)), 11)
- Equals(LengthOf(Line(K, L)), 11)
- Equals(MeasureOf(Angle(K, J, L)), 60)
- PointLiesOnLine(M, Line(L, J))
- Equals(LengthOf(Line(M, L)), 5.5)
- Perpendicular(Line(K, M), Line(L, M))
Find $JM$. | 5.5 | [
"Find(LengthOf(Line(J,M)))"
] | [
"Equals(LengthOf(Line(K, J)), 11)",
"Equals(LengthOf(Line(K, L)), 11)",
"Equals(MeasureOf(Angle(K, J, L)), 60)",
"PointLiesOnLine(M, Line(L, J))",
"Equals(LengthOf(Line(M, L)), 5.5)",
"Perpendicular(Line(K, M), Line(L, M))"
] | [
"JM",
"KJ",
"KL",
"KM",
"LJ",
"LM"
] | {"J": [0.0, 236.0], "K": [136.0, 1.0], "L": [271.0, 234.0], "M": [136.0, 235.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, F)), 4.2)
- Equals(LengthOf(Line(B, D)), 5.4)
- Perpendicular(Line(E, B), Line(B, D))
- Equals(LengthOf(Line(E, B)), LengthOf(Line(D, F)))
- Equals(LengthOf(Line(E, F)), LengthOf(Line(D, B)))
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 19.2 | [
"Find(PerimeterOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(D, F)), 4.2)",
"Equals(LengthOf(Line(B, D)), 5.4)",
"Perpendicular(Line(E, B), Line(B, D))",
"Equals(LengthOf(Line(E, B)), LengthOf(Line(D, F)))",
"Equals(LengthOf(Line(E, F)), LengthOf(Line(D, B)))"
] | [
"BD",
"EB",
"EF",
"FD"
] | {"B": [1.0, 145.0], "D": [173.0, 147.0], "E": [1.0, 12.0], "F": [172.0, 18.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(X, W, Z)), 105)
- Equals(LengthOf(Line(Y, X)), 24)
- Equals(LengthOf(Line(Y, Z)), 28)
Use parallelogram WXYZ to find $m\angle WZY$ | 75 | [
"Parallelogram(W,X,Y,Z)",
"Find(MeasureOf(Angle(W,Z,Y)))"
] | [
"Equals(MeasureOf(Angle(X, W, Z)), 105)",
"Equals(LengthOf(Line(Y, X)), 24)",
"Equals(LengthOf(Line(Y, Z)), 28)"
] | [
"ZW",
"XW",
"YZ",
"YX"
] | {"Z": [1.0, 177.0], "W": [84.0, 3.0], "X": [334.0, 1.0], "Y": [251.0, 175.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 13)
- Equals(LengthOf(Line(A, C)), 7)
- Equals(LengthOf(Line(F, E)), 14)
- Equals(LengthOf(Line(C, B)), 10)
Find the perimeter of $\triangle D E F,$ if $\triangle D E F \sim \triangle A C B$ | 42 | [
"Similar(Triangle(D,E,F),Triangle(A,C,B))",
"Find(PerimeterOf(Triangle(D,E,F)))"
] | [
"Equals(LengthOf(Line(A, B)), 13)",
"Equals(LengthOf(Line(A, C)), 7)",
"Equals(LengthOf(Line(F, E)), 14)",
"Equals(LengthOf(Line(C, B)), 10)"
] | [
"DE",
"FD",
"FE"
] | {"D": [85.0, 1.0], "E": [98.0, 144.0], "F": [1.0, 171.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, C, A)), 3x)
- Equals(MeasureOf(Angle(A, B, C)), 4x)
- Equals(MeasureOf(Angle(C, A, B)), 5x)
- PointLiesOnLine(D, Line(B, C))
Find $x$. | 15 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, C, A)), 3x)",
"Equals(MeasureOf(Angle(A, B, C)), 4x)",
"Equals(MeasureOf(Angle(C, A, B)), 5x)",
"PointLiesOnLine(D, Line(B, C))"
] | [
"AB",
"AC",
"BC",
"BD",
"CD"
] | {"A": [213.72547838356297, 350.00016382093844], "B": [568.7253304683094, 350.7936638731708], "C": [1.0, 0.0], "D": [457.0, 279.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), 21)
- Equals(LengthOf(Line(B, G)), 14)
- Equals(LengthOf(Line(G, H)), 8)
- Equals(LengthOf(Line(E, C)), 24)
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnLine(G, Line(A, F))
- PointLiesOnLine(G, Line(B, H))
- PointLiesOnLine(H, Line(C, E))
- Perpendicular(Line(G, H), L... | 474 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(D, B)), 21)",
"Equals(LengthOf(Line(B, G)), 14)",
"Equals(LengthOf(Line(G, H)), 8)",
"Equals(LengthOf(Line(E, C)), 24)",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(G, Line(A, F))",
"PointLiesOnLine(G, Line(B, H))",
"PointLiesOnLine(H, Line(C, E))",
"Perpendicular(Line(G... | [
"AD",
"AE",
"BC",
"DB",
"EC",
"BF",
"FC",
"CH",
"HE",
"GA",
"GB",
"GF",
"GH",
"BH",
"AF"
] | {"A": [181.0, 112.0], "B": [64.0, 2.0], "C": [0.0, 168.0], "D": [223.0, 0.0], "E": [183.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(S, U, V)), 2x+15)
- Equals(MeasureOf(Angle(S, T, B)), 3x-5)
- PointLiesOnLine(B, Line(V, T))
- PointLiesOnLine(B, Line(U, S))
- PointLiesOnCircle(V, Circle(A, radius_4_0))
- PointLiesOnCircle(T, Circle(A, radius_4_0))
- PointLiesOnCircle(S, Circle(A, radius_4_0))
- PointLies... | 24 | [
"Equals(MeasureOf(Angle(S)),3x)",
"Equals(MeasureOf(Angle(V)),x+16)",
"Find(MeasureOf(Angle(S)))"
] | [
"Equals(MeasureOf(Angle(S, U, V)), 2x+15)",
"Equals(MeasureOf(Angle(S, T, B)), 3x-5)",
"PointLiesOnLine(B, Line(V, T))",
"PointLiesOnLine(B, Line(U, S))",
"PointLiesOnCircle(V, Circle(A, radius_4_0))",
"PointLiesOnCircle(T, Circle(A, radius_4_0))",
"PointLiesOnCircle(S, Circle(A, radius_4_0))",
"Point... | [
"BS",
"TB",
"TS",
"UB",
"US",
"VB",
"VT",
"VU"
] | {"A": [168.0, 160.0], "B": [147.0, 93.0], "S": [69.0, 281.0], "T": [82.0, 28.0], "U": [184.0, 3.0], "V": [303.0, 241.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, E, D)), 2x)
- Equals(MeasureOf(Angle(M, F, E)), 52)
- Equals(MeasureOf(Angle(J, D, I)), 88)
- Equals(MeasureOf(Angle(G, H, M)), x+2)
- Equals(MeasureOf(Angle(G, B, I)), x+10)
- PointLiesOnLine(H, Line(B, G))
- PointLiesOnLine(B, Line(D, I))
- PointLiesOnLine(F, Line(H, M)... | 52 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, E, D)), 2x)",
"Equals(MeasureOf(Angle(M, F, E)), 52)",
"Equals(MeasureOf(Angle(J, D, I)), 88)",
"Equals(MeasureOf(Angle(G, H, M)), x+2)",
"Equals(MeasureOf(Angle(G, B, I)), x+10)",
"PointLiesOnLine(H, Line(B, G))",
"PointLiesOnLine(B, Line(D, I))",
"PointLiesOnLine(F, Line(H... | [
"ED",
"DJ",
"EJ",
"AE",
"EF",
"AF",
"MF",
"FH",
"MH",
"GH",
"HB",
"GB",
"BI",
"BD",
"DI"
] | {"A": [118.0, 1.0], "B": [221.0, 262.0], "D": [290.0, 127.0], "E": [110.0, 26.0], "F": [68.0, 165.0], "G": [3.0, 260.0], "H": [139.0, 262.0], "I": [188.0, 324.0], "J": [353.0, 164.0], "M": [6.0, 79.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 3.5)
- Equals(LengthOf(Line(A, B)), 3)
- Equals(LengthOf(Line(A, C)), 5)
- Equals(LengthOf(Line(D, E)), 3)
- Equals(LengthOf(Line(A, E)), y)
- Equals(LengthOf(Line(B, E)), x)
- PointLiesOnLine(B, Line(C, A))
- PointLiesOnLine(E, Line(A, D))
- Parallel(Line(B, E), Line(... | 2.1 | [
"Find(LengthOf(Line(B,E)))"
] | [
"Equals(LengthOf(Line(C, D)), 3.5)",
"Equals(LengthOf(Line(A, B)), 3)",
"Equals(LengthOf(Line(A, C)), 5)",
"Equals(LengthOf(Line(D, E)), 3)",
"Equals(LengthOf(Line(A, E)), y)",
"Equals(LengthOf(Line(B, E)), x)",
"PointLiesOnLine(B, Line(C, A))",
"PointLiesOnLine(E, Line(A, D))",
"Parallel(Line(B, E)... | [
"AB",
"AC",
"AD",
"AE",
"BC",
"BE",
"CD",
"ED"
] | {"A": [57.0, 281.0], "B": [250.0, 166.0], "C": [373.0, 94.0], "D": [592.0, 244.0], "E": [388.0, 258.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, A, T)), 48)
- PointLiesOnLine(A, Line(R, S))
- PointLiesOnCircle(S, Circle(A, radius_2_0))
- PointLiesOnCircle(T, Circle(A, radius_2_0))
- PointLiesOnCircle(R, Circle(A, radius_2_0))
Find $m \angle S$. | 66 | [
"Find(MeasureOf(Angle(S)))"
] | [
"Equals(MeasureOf(Angle(R, A, T)), 48)",
"PointLiesOnLine(A, Line(R, S))",
"PointLiesOnCircle(S, Circle(A, radius_2_0))",
"PointLiesOnCircle(T, Circle(A, radius_2_0))",
"PointLiesOnCircle(R, Circle(A, radius_2_0))"
] | [
"AS",
"RA",
"RS",
"ST"
] | {"A": [159.0, 157.0], "R": [168.0, 6.0], "S": [150.0, 314.0], "T": [267.0, 273.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(J, Line(L, N))
- PointLiesOnLine(J, Line(M, P))
Use rectangle LMNP, parallelogram LKMJ to solve the problem.
If $M K=6 x, K L=3 x+2 y,$ and $J N=14-x$
find $y$ | 3 | [
"Rectangle(L,M,N,P)",
"Parallelogram(L,K,M,J)",
"Equals(LengthOf(Line(M,K)),6x)",
"Equals(LengthOf(Line(K,L)),3x+2y)",
"Equals(LengthOf(Line(J,N)),14-x)",
"Find(y)"
] | [
"PointLiesOnLine(J, Line(L, N))",
"PointLiesOnLine(J, Line(M, P))"
] | [
"LN",
"LM",
"LP",
"LK",
"LJ",
"NM",
"NP",
"NJ",
"MP",
"MK",
"MJ",
"PJ"
] | {"L": [121.52729015752848, 1.5402691564575832], "N": [0.0, 154.0], "M": [122.45922975297927, 152.2923667827388], "P": [1.4878615811037008, 0.6231055033433108], "K": [185.3587452848918, 76.69724042088545], "J": [61.5, 77.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, G)), 3)
- Equals(LengthOf(Line(F, B)), 4)
- Equals(LengthOf(Line(F, C)), 2)
- Equals(LengthOf(Line(E, C)), 1)
- PointLiesOnLine(H, Line(D, F))
- PointLiesOnLine(I, Line(D, F))
- PointLiesOnLine(H, Line(D, I))
- PointLiesOnLine(C, Line(F, E))
- PointLiesOnLine(I, Line(F, H))... | \frac { 3 } { 2 } | [
"Similar(Triangle(A,B,C),Triangle(D,E,F))",
"Equals(Line(B,G),AltitudeOf(Triangle(A,B,C)))",
"Equals(Line(E,H),AltitudeOf(Triangle(D,E,F)))",
"Equals(LengthOf(Line(B,G)),3)",
"Equals(LengthOf(Line(B,F)),4)",
"Equals(LengthOf(Line(F,C)),2)",
"Equals(LengthOf(Line(C,E)),1)",
"Find(LengthOf(Line(E,H)))"
... | [
"Equals(LengthOf(Line(B, G)), 3)",
"Equals(LengthOf(Line(F, B)), 4)",
"Equals(LengthOf(Line(F, C)), 2)",
"Equals(LengthOf(Line(E, C)), 1)",
"PointLiesOnLine(H, Line(D, F))",
"PointLiesOnLine(I, Line(D, F))",
"PointLiesOnLine(H, Line(D, I))",
"PointLiesOnLine(C, Line(F, E))",
"PointLiesOnLine(I, Line... | [
"AC",
"AG",
"BA",
"BC",
"BG",
"CG",
"DE",
"DF",
"DH",
"DI",
"EB",
"EC",
"EH",
"FB",
"FC",
"FE",
"FH",
"FI",
"HI",
"IA",
"IC",
"IG"
] | {"A": [0.0, 0.0], "B": [1.0, 172.0], "C": [301.0, 172.0], "D": [347.0, 88.0], "E": [345.0, 172.0], "F": [201.0, 172.0], "G": [75.0, 43.0], "H": [311.0, 108.0], "I": [251.0, 144.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 27 | [
"Equals(MeasureOf(Angle(1)),3a+40)",
"Equals(MeasureOf(Angle(2)),2a+25)",
"Equals(MeasureOf(Angle(3)),5b-26)",
"Find(b)"
] | [
"Equals(MeasureOf(Angle(L, W, N)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, X, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(I, Y, L)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(L, Y, Z)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(K, Y, M)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"GN",
"GW",
"GX",
"HE",
"HZ",
"HZ",
"IK",
"IY",
"IZ",
"ML",
"MW",
"MY",
"WL",
"WN",
"WX",
"XE",
"XN",
"YK",
"YL",
"YW",
"YZ",
"ZE",
"ZK",
"ZX"
] | {"E": [331.0, 74.0], "G": [57.0, 80.0], "H": [165.0, 365.0], "I": [1.0, 198.0], "K": [295.0, 360.0], "L": [184.0, 6.0], "M": [23.0, 289.0], "N": [358.0, 248.0], "W": [122.0, 116.0], "X": [261.0, 194.0], "Y": [58.0, 228.0], "Z": [199.0, 305.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 6)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(LengthOf(Line(S, A)), z)
- Equals(LengthOf(Line(S, B)), x)
- PointLiesOnLine(C, Line(S, B))
- Perpendicular(Line(S, C), Line(A, C))
- Perpendicular(Line(A, B), Line(S, A))
Find y | 10 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), 6)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(S, A)), z)",
"Equals(LengthOf(Line(S, B)), x)",
"PointLiesOnLine(C, Line(S, B))",
"Perpendicular(Line(S, C), Line(A, C))",
"Perpendicular(Line(A, B), Line(S, A))"
] | [
"AB",
"AC",
"BC",
"SA",
"SB",
"SC"
] | {"A": [0.0, 125.0], "B": [1.0, 1.0], "C": [46.0, 21.0], "S": [284.0, 127.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, C, E)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(D, E, B)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 40 | [
"Rectangle(A,B,C,D)",
"Equals(MeasureOf(Angle(2)),40)",
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, C, E)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(D, E, B)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AE",
"BA",
"BC",
"BD",
"BE",
"CA",
"CD",
"CE",
"DA",
"DE"
] | {"A": [1.0, 1.0], "B": [2.0, 118.0], "C": [236.0, 1.0], "D": [236.0, 119.0], "E": [118.0, 60.0]} | [
""
] |
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