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(D, A)), 8)
- Equals(LengthOf(Line(D, H)), x)
- Equals(MeasureOf(Angle(D, A, B)), 30)
- Equals(MeasureOf(Angle(A, B, C)), 45)
- Equals(LengthOf(Line(H, F)), 6)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(H, Line(A, B))
- PointLiesOnLine(H, Line(A, F))
- PointLiesOnLine(F... | 4 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(D, A)), 8)",
"Equals(LengthOf(Line(D, H)), x)",
"Equals(MeasureOf(Angle(D, A, B)), 30)",
"Equals(MeasureOf(Angle(A, B, C)), 45)",
"Equals(LengthOf(Line(H, F)), 6)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(H, Line(A, F))",
"PointLiesO... | [
"AB",
"AF",
"AH",
"BF",
"CB",
"CF",
"DA",
"DC",
"DH",
"HB",
"HF"
] | {"A": [0.0, 117.0], "B": [467.0, 116.0], "C": [359.0, 8.0], "D": [193.0, 7.0], "F": [357.0, 116.0], "H": [194.0, 117.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, E, D)), 2y)
- Equals(MeasureOf(Angle(F, D, E)), 110)
- Equals(MeasureOf(Angle(E, C, F)), 78)
- Equals(MeasureOf(Angle(C, F, D)), x+36)
- Parallel(Line(C, E), Line(F, D))
Find $x$. | 66 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, E, D)), 2y)",
"Equals(MeasureOf(Angle(F, D, E)), 110)",
"Equals(MeasureOf(Angle(E, C, F)), 78)",
"Equals(MeasureOf(Angle(C, F, D)), x+36)",
"Parallel(Line(C, E), Line(F, D))"
] | [
"CF",
"DE",
"EC",
"FD"
] | {"C": [2.0, 270.0], "D": [388.0, 121.0], "E": [58.0, 2.0], "F": [358.0, 270.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(LengthOf(Line(B, C)), 15)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 17 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(B, C)), 15)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.33345410291426, 0.6509666211458267], "B": [274.9458917461828, 130.32331570454525], "C": [0.6743400348032225, 129.00246214224887]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 5)
- Equals(LengthOf(Line(D, B)), 10)
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLine(F, Line(C, B))
- PointLiesOnLine(E, Line(D, B))
- PointLiesOnCircle(E, Circle(O, radius_4_0))
- PointLiesOnCircle(F, Circle(O, radius_4_0))
- PointLiesOnCircle(G, Circle(O, radius_... | 30.4 | [
"Regular(Polygon($))",
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(A, D)), 5)",
"Equals(LengthOf(Line(D, B)), 10)",
"PointLiesOnLine(G, Line(A, C))",
"PointLiesOnLine(F, Line(C, B))",
"PointLiesOnLine(E, Line(D, B))",
"PointLiesOnCircle(E, Circle(O, radius_4_0))",
"PointLiesOnCircle(F, Circle(O, radius_4_0))",
"PointLiesOnCircle(G, Circle(O, rad... | [
"AC",
"AD",
"AG",
"BE",
"BF",
"CB",
"CF",
"CG",
"DB",
"DE",
"GF"
] | {"A": [211.0, 2.0], "B": [0.0, 105.0], "C": [0.0, 0.0], "D": [212.0, 106.0], "E": [52.0, 104.0], "F": [0.0, 52.0], "G": [53.0, 1.0], "O": [53.0, 52.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, A)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, C, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(G, C, F)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(E, C, G)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 17 | [
"Isosceles(Triangle(A,B,C))",
"Equilateral(Triangle(D,C,E))",
"Isosceles(Triangle(F,C,G))",
"Equals(Angle(4),Angle(C))",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(D, C, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, C, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(G, C, F)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(E, C, G)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(B, C, E)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AF",
"AG",
"BA",
"BF",
"BG",
"CA",
"CB",
"CD",
"CE",
"CF",
"CG",
"DA",
"DB",
"DF",
"DG",
"EA",
"EB",
"ED",
"EF",
"EG",
"FG"
] | {"A": [0.0, 233.0], "B": [518.0, 233.0], "C": [259.0, 1.0], "D": [103.0, 233.0], "E": [413.0, 233.0], "F": [208.0, 233.0], "G": [311.0, 233.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 12)
- Equals(LengthOf(Line(C, E)), 6)
- Equals(LengthOf(Line(A, D)), x)
- Equals(LengthOf(Line(E, F)), y)
- Equals(LengthOf(Line(F, H)), 3)
- Equals(LengthOf(Line(B, F)), 2)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(F, Line(B, D))
- PointLiesOnLine(E, Line(C, ... | 22.5 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, C)), 12)",
"Equals(LengthOf(Line(C, E)), 6)",
"Equals(LengthOf(Line(A, D)), x)",
"Equals(LengthOf(Line(E, F)), y)",
"Equals(LengthOf(Line(F, H)), 3)",
"Equals(LengthOf(Line(B, F)), 2)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(F, Line(B, D))",
"PointLiesOnLine(E, L... | [
"AB",
"AC",
"AD",
"AF",
"AG",
"BD",
"BF",
"BH",
"CE",
"CF",
"CG",
"CH",
"DF",
"FE",
"FH",
"HE"
] | {"A": [84.0, 2.0], "B": [88.0, 171.0], "C": [170.0, 0.0], "D": [90.0, 86.0], "E": [152.0, 29.0], "F": [87.0, 135.0], "G": [52.0, 6.0], "H": [66.0, 169.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), z)
- Equals(LengthOf(Line(B, D)), 8)
- Equals(LengthOf(Line(A, B)), y)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Equals(MeasureOf(Angle(B, D, A)), 60)
- Equals(LengthOf(Line(A, D)), x)
- Perpendicular(Line(B, C), Line(A, C))
- Perpendicular(Line(A, B), Line(A, D))
Fin... | 4 \sqrt { 3 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), z)",
"Equals(LengthOf(Line(B, D)), 8)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Equals(MeasureOf(Angle(B, D, A)), 60)",
"Equals(LengthOf(Line(A, D)), x)",
"Perpendicular(Line(B, C), Line(A, C))",
"Perpendicular(Line(A, B), Line(A, D))"... | [
"AB",
"AC",
"AD",
"BC",
"BD"
] | {"A": [128.83179792830194, 219.33187314906218], "B": [128.67133250256126, 1.5536783226083486], "C": [236.50898890208444, 110.49547483516933], "D": [0.19786910197868224, 220.33333333333331]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(X, Y)), 2x+3)
- Equals(LengthOf(Line(A, Y)), 4x-1)
- Equals(LengthOf(Line(X, Y)), LengthOf(Line(A, Y)))
Find $XZ$ of isosceles $\triangle XYZ$ | 12 | [
"Isosceles(Triangle(X,Y,Z))",
"Find(LengthOf(Line(X,Z)))"
] | [
"Equals(LengthOf(Line(X, Y)), 2x+3)",
"Equals(LengthOf(Line(A, Y)), 4x-1)",
"Equals(LengthOf(Line(X, Y)), LengthOf(Line(A, Y)))"
] | [
"AX",
"AY",
"XY"
] | {"A": [289.0, 110.0], "X": [0.0, 110.0], "Y": [145.99656357388315, 0.252004581901474]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, C, D)), 66)
- Equals(MeasureOf(Angle(C, D, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(B, D, A)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(D, B, C)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(D, A, B)), 24)
- Equals(MeasureOf(Angle(A, B, D)), MeasureOf(angle ... | 24 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(B, C, D)), 66)",
"Equals(MeasureOf(Angle(C, D, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(B, D, A)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(D, B, C)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(D, A, B)), 24)",
"Equals(MeasureOf(Angle(A, B, D)), MeasureOf(angle 2)... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [2.2132352941176237, 269.00735294117646], "B": [600.9234345586568, 270.49808450019486], "C": [601.998767948655, 0.6672192478346801], "D": [363.5242226421577, 107.36122904753725]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x+1)
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(A, C)), 2\sqrt{2})
- Perpendicular(Line(B, C), Line(A, C))
Find x. | 0.5 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x+1)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(A, C)), 2\\sqrt{2})",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [166.0, 195.0], "B": [1.0, 1.0], "C": [1.0, 194.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, H)), y)
- Equals(LengthOf(Line(Q, J)), 2z)
- Equals(LengthOf(Line(Q, P)), 2x-6)
- Equals(LengthOf(Line(Q, K)), 7)
- Equals(LengthOf(Line(Q, L)), 3)
- Equals(LengthOf(Line(Q, M)), 4)
- PointLiesOnLine(J, Line(K, H))
- PointLiesOnLine(L, Line(K, M))
- PointLiesOnLine(Q, Line(... | 4.75 | [
"IsMidpointOf(Point(J),Line(K,H))",
"IsMidpointOf(Point(P),Line(H,M))",
"IsMidpointOf(Point(L),Line(M,K))",
"Find(x)"
] | [
"Equals(LengthOf(Line(Q, H)), y)",
"Equals(LengthOf(Line(Q, J)), 2z)",
"Equals(LengthOf(Line(Q, P)), 2x-6)",
"Equals(LengthOf(Line(Q, K)), 7)",
"Equals(LengthOf(Line(Q, L)), 3)",
"Equals(LengthOf(Line(Q, M)), 4)",
"PointLiesOnLine(J, Line(K, H))",
"PointLiesOnLine(L, Line(K, M))",
"PointLiesOnLine(Q... | [
"HJ",
"HL",
"HM",
"HP",
"KH",
"KJ",
"KL",
"KM",
"KP",
"MJ",
"ML",
"MP",
"QH",
"QJ",
"QK",
"QL",
"QM",
"QP"
] | {"H": [512.0, 2.0], "J": [258.0, 100.0], "K": [0.0, 200.0], "L": [238.0, 263.0], "M": [469.0, 323.0], "P": [491.0, 164.0], "Q": [329.0, 176.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 8)
- Equals(LengthOf(Line(D, C)), 4)
- Equals(LengthOf(Line(E, D)), 6)
- Equals(LengthOf(Line(R, S)), 3)
- Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))
- Equals(LengthOf(Line(E, A)), LengthOf(Line(D, C)))
- Equals(LengthOf(Line(P, Q)), LengthOf(Line(Q, R)))
- Equ... | \frac { 4 } { 3 } | [
"Similar(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T))",
"Find(ScaleFactorOf(Pentagon(A,B,C,D,E),Pentagon(P,Q,R,S,T)))"
] | [
"Equals(LengthOf(Line(B, A)), 8)",
"Equals(LengthOf(Line(D, C)), 4)",
"Equals(LengthOf(Line(E, D)), 6)",
"Equals(LengthOf(Line(R, S)), 3)",
"Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))",
"Equals(LengthOf(Line(E, A)), LengthOf(Line(D, C)))",
"Equals(LengthOf(Line(P, Q)), LengthOf(Line(Q, R)))",
... | [
"BA",
"CB",
"DC",
"DE",
"EA",
"PQ",
"QR",
"RS",
"ST",
"TP"
] | {"A": [1.0, 152.0], "B": [207.0, 2.0], "C": [414.0, 150.0], "D": [307.0, 296.0], "E": [104.0, 295.0], "P": [414.0, 550.0], "Q": [207.0, 402.0], "R": [1.0, 552.0], "S": [104.0, 695.0], "T": [307.0, 696.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(E, G))
- PointLiesOnLine(A, Line(D, F))
- Perpendicular(Line(D, G), Line(G, F))
Quadrilateral DEFG is a rectangle. If $FD = 3x - 7$ and $EG = x + 5$, find $EG$. | 6 | [
"Rectangle(D,E,F,G)",
"Equals(LengthOf(Line(F,D)),3x-7)",
"Equals(LengthOf(Line(E,G)),x+5)",
"Find(LengthOf(Line(E,G)))"
] | [
"PointLiesOnLine(A, Line(E, G))",
"PointLiesOnLine(A, Line(D, F))",
"Perpendicular(Line(D, G), Line(G, F))"
] | [
"DA",
"DF",
"DG",
"EA",
"ED",
"EF",
"EG",
"FA",
"FG",
"GA"
] | {"A": [136.0, 64.0], "D": [1.0, 1.0], "E": [272.0, 1.0], "F": [273.0, 126.0], "G": [0.0, 127.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, E, A)), 120)
- PointLiesOnLine(X, Line(E, C))
- PointLiesOnLine(X, Line(F, G))
- PointLiesOnLine(X, Line(C, D))
- PointLiesOnLine(E, Line(A,Z))
- Parallel(Line(F,G), Line(A,Z))
Find the value of $x$ in the figure below. | 128 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, E, A)), 120)",
"PointLiesOnLine(X, Line(E, C))",
"PointLiesOnLine(X, Line(F, G))",
"PointLiesOnLine(X, Line(C, D))",
"PointLiesOnLine(E, Line(A,Z))",
"Parallel(Line(F,G), Line(A,Z))"
] | [
"AE",
"CD",
"EC",
"ED",
"EX",
"FG",
"FX",
"XC",
"XD",
"XG",
"EZ",
"AZ"
] | {"A": [39.0, 161.0], "C": [2.0, 0.0], "D": [215.0, 160.0], "E": [159.0, 111.0], "F": [0.0, 97.0], "G": [197.0, 13.0], "X": [83.0, 61.0], "Z": [123.0, 232.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, L)), 3y)
- Equals(LengthOf(Line(L, J)), 7)
- Equals(LengthOf(Line(L, M)), 9x)
- Equals(LengthOf(Line(K, N)), 36)
- Equals(LengthOf(Line(N, J)), y+15)
- PointLiesOnLine(J, Line(K, M))
- PointLiesOnLine(J, Line(L, N))
If KLMN is a parallelogram, find the value of the
indica... | 11 | [
"Parallelogram(K,L,M,N)",
"Find(y)"
] | [
"Equals(LengthOf(Line(K, L)), 3y)",
"Equals(LengthOf(Line(L, J)), 7)",
"Equals(LengthOf(Line(L, M)), 9x)",
"Equals(LengthOf(Line(K, N)), 36)",
"Equals(LengthOf(Line(N, J)), y+15)",
"PointLiesOnLine(J, Line(K, M))",
"PointLiesOnLine(J, Line(L, N))"
] | [
"KJ",
"KL",
"KM",
"KN",
"LJ",
"LM",
"LN",
"MJ",
"NJ",
"NM"
] | {"J": [181.0, 72.0], "K": [0.0, 4.0], "L": [270.0, 1.0], "M": [359.0, 138.0], "N": [92.0, 142.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, B)), 5)
- Equals(MeasureOf(Angle(A, T, B)), 135)
- PointLiesOnLine(T, Line(A, R))
What is the length of $R T ?$ | 5 \sqrt { 2 } | [
"Find(LengthOf(Line(R,T)))"
] | [
"Equals(LengthOf(Line(T, B)), 5)",
"Equals(MeasureOf(Angle(A, T, B)), 135)",
"PointLiesOnLine(T, Line(A, R))"
] | [
"AR",
"AT",
"RB",
"RT",
"TB"
] | {"A": [177.0, 178.0], "B": [1.0, 134.0], "R": [0.0, 0.0], "T": [137.0, 138.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, F, D)), MeasureOf(Angle(8)))
- PointLiesOnLine(B, Line(A, E))
- PointLiesOnLine(A, Line(E, F))
- PointLiesOnLine(A, Line(B, F))
- PointLiesOnLine(B, Line(E, F))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(F, Circle(A, radius_0_0))
Find $\angle 8$ | 90 | [
"Find(MeasureOf(Angle(8)))"
] | [
"Equals(MeasureOf(Angle(B, F, D)), MeasureOf(Angle(8)))",
"PointLiesOnLine(B, Line(A, E))",
"PointLiesOnLine(A, Line(E, F))",
"PointLiesOnLine(A, Line(B, F))",
"PointLiesOnLine(B, Line(E, F))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(F, Circle(A, radius_0_0))"
] | [
"AB",
"AE",
"AF",
"BE",
"BF",
"EF",
"FD"
] | {"A": [59.0, 51.0], "B": [63.0, 97.0], "D": [1.0, 6.0], "E": [62.0, 136.0], "F": [62.0, 6.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, L)), 6)
- Equals(LengthOf(Line(P, N)), 11)
- Equals(LengthOf(Line(E, F)), 6)
- Equals(LengthOf(Line(J, Q)), 12)
- PointLiesOnLine(N, Line(G, I))
- PointLiesOnLine(P, Line(G, I))
- PointLiesOnLine(M, Line(G, L))
- PointLiesOnLine(P, Line(G, N))
- PointLiesOnLine(A, Line(P, D... | 20 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(G, L)), 6)",
"Equals(LengthOf(Line(P, N)), 11)",
"Equals(LengthOf(Line(E, F)), 6)",
"Equals(LengthOf(Line(J, Q)), 12)",
"PointLiesOnLine(N, Line(G, I))",
"PointLiesOnLine(P, Line(G, I))",
"PointLiesOnLine(M, Line(G, L))",
"PointLiesOnLine(P, Line(G, N))",
"PointLiesOnLine(A, Li... | [
"AG",
"AM",
"AP",
"BE",
"BH",
"BJ",
"BK",
"BR",
"BS",
"CI",
"CN",
"CQ",
"DF",
"DL",
"DO",
"EF",
"EH",
"EJ",
"EK",
"ER",
"ES",
"FL",
"GD",
"GI",
"GL",
"GM",
"GN",
"GP",
"HI",
"HJ",
"HK",
"HQ",
"HR",
"HS",
"IN",
"IQ",
"JI",
"JK",
"JQ",
"JR"... | {"A": [22.0, 22.0], "B": [176.0, 161.0], "C": [21.0, 162.0], "D": [98.0, 22.0], "E": [195.0, 116.0], "F": [100.0, 114.0], "G": [1.0, 1.0], "H": [196.0, 180.0], "I": [2.0, 182.0], "J": [173.0, 181.0], "K": [176.0, 115.0], "L": [97.0, 1.0], "M": [24.0, 1.0], "N": [1.0, 162.0], "O": [77.0, 21.0], "P": [2.0, 20.0], "Q": [2... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x-5)
- Equals(LengthOf(Line(B, C)), 54)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(B, D)), 28)
- PointLiesOnLine(D, Line(B, C))
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(Angle(D, A, B)))
Find $x$. | 70 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x-5)",
"Equals(LengthOf(Line(B, C)), 54)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, D)), 28)",
"PointLiesOnLine(D, Line(B, C))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(Angle(D, A, B)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [382.0, 31.0], "B": [88.0, 312.0], "C": [86.0, 2.0], "D": [88.0, 122.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 13)
- Equals(LengthOf(Line(B, C)), 15)
- Equals(LengthOf(Line(C, A)), 12)
Find the measure of $\angle A$. Round to the nearest degree. | 74 | [
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(B, A)), 13)",
"Equals(LengthOf(Line(B, C)), 15)",
"Equals(LengthOf(Line(C, A)), 12)"
] | [
"BC",
"BA",
"CA"
] | {"B": [54.065108514190314, 0.43628269337784786], "C": [170.7116859151793, 183.01705322770513], "A": [2.6632852126414264, 185.01196514501237]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, B, C)), x-8)
- Equals(MeasureOf(Angle(F, A, B)), x+2)
- Equals(MeasureOf(Angle(B, C, D)), x+7)
- Equals(MeasureOf(Angle(A, F, E)), x-4)
- Equals(MeasureOf(Angle(F, E, D)), x+6)
- Equals(MeasureOf(Angle(C, E, D)), x-3)
Find $m\angle B$ | 112 | [
"Find(MeasureOf(Angle(B)))"
] | [
"Equals(MeasureOf(Angle(A, B, C)), x-8)",
"Equals(MeasureOf(Angle(F, A, B)), x+2)",
"Equals(MeasureOf(Angle(B, C, D)), x+7)",
"Equals(MeasureOf(Angle(A, F, E)), x-4)",
"Equals(MeasureOf(Angle(F, E, D)), x+6)",
"Equals(MeasureOf(Angle(C, E, D)), x-3)"
] | [
"AB",
"BC",
"CD",
"DE",
"EF",
"FA"
] | {"A": [85.0, 2.0], "B": [255.0, 2.0], "C": [337.0, 112.0], "D": [255.0, 232.0], "E": [90.0, 234.0], "F": [1.0, 117.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 8)
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(B, C, A)), 43)
- Equals(LengthOf(Line(B, D)), y)
- PointLiesOnLine(A, Line(C, D))
- Perpendicular(Line(A, C), Line(A, B))
- Perpendicular(Line(B, D), Line(B, C))
Find y. Round to the nearest tenth. | 11.7 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(B, C, A)), 43)",
"Equals(LengthOf(Line(B, D)), y)",
"PointLiesOnLine(A, Line(C, D))",
"Perpendicular(Line(A, C), Line(A, B))",
"Perpendicular(Line(B, D), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [137.00160132781633, 0.7662061388129189], "B": [136.3578479762261, 145.01323386956474], "C": [293.36457422764033, 0.3320890526929148], "D": [0.0, 0.9999999999999929]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, J)), 24)
- Equals(LengthOf(Line(L, J)), 17)
- Perpendicular(Line(L, J), Line(L, K))
Use a calculator to find the measure of $∠J$ to the nearest degree. | 45 | [
"Find(MeasureOf(Angle(J)))"
] | [
"Equals(LengthOf(Line(K, J)), 24)",
"Equals(LengthOf(Line(L, J)), 17)",
"Perpendicular(Line(L, J), Line(L, K))"
] | [
"LK",
"LJ",
"KJ"
] | {"L": [62.59970879497045, 124.86500429093503], "K": [283.0, 13.0], "J": [0.8427131760561224, 0.688265811941136]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 25)
- Equals(LengthOf(Line(A, B)), 15)
- Equals(LengthOf(Line(C, B)), 20)
- Perpendicular(Line(A, B), Line(C, B))
Express the ratio of $\sin A$ as a decimal to the nearest hundredth. | 0.80 | [
"Find(RatioOf(SinOf(Angle(A))))"
] | [
"Equals(LengthOf(Line(A, C)), 25)",
"Equals(LengthOf(Line(A, B)), 15)",
"Equals(LengthOf(Line(C, B)), 20)",
"Perpendicular(Line(A, B), Line(C, B))"
] | [
"AB",
"AC",
"CB"
] | {"A": [238.0, 1.0], "B": [236.0, 131.0], "C": [3.0, 132.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(Z, X))
- PointLiesOnLine(T, Line(W, Y))
- Perpendicular(Line(X, W), Line(X, Y))
- Perpendicular(Line(X, W), Line(Z, W))
- Perpendicular(Line(X, Y), Line(Z, Y))
- Perpendicular(Line(Z, W), Line(Z, Y))
WXYZ is a square. If $WT = 3$, find $m \angle WTZ$ | 90 | [
"Square(W,X,Y,Z)",
"Equals(LengthOf(Line(W,T)),3)",
"Find(MeasureOf(Angle(W,T,Z)))"
] | [
"PointLiesOnLine(T, Line(Z, X))",
"PointLiesOnLine(T, Line(W, Y))",
"Perpendicular(Line(X, W), Line(X, Y))",
"Perpendicular(Line(X, W), Line(Z, W))",
"Perpendicular(Line(X, Y), Line(Z, Y))",
"Perpendicular(Line(Z, W), Line(Z, Y))"
] | [
"ZX",
"ZT",
"ZW",
"ZY",
"XT",
"XW",
"XY",
"TW",
"TY",
"WY"
] | {"Z": [142.33333333333331, 143.0], "X": [1.4896551724137765, 0.4931034482758747], "T": [71.74560800863676, 72.25085876926097], "W": [142.6735959307499, 0.8218706793993817], "Y": [-1.4210854715202004e-14, 143.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, C)), 2x)
- Equals(MeasureOf(Angle(C, A, D)), 3x)
- Perpendicular(Line(A, B), Line(A, D))
Find x | 18 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, A, C)), 2x)",
"Equals(MeasureOf(Angle(C, A, D)), 3x)",
"Perpendicular(Line(A, B), Line(A, D))"
] | [
"AB",
"AC",
"AD"
] | {"A": [7.0, 144.0], "B": [6.0, 1.0], "C": [94.0, 25.0], "D": [163.0, 145.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, B, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(B, F, M)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(G, B, L)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(M, F, T)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 105 | [
"Equals(MeasureOf(Angle(9)),75)",
"Find(MeasureOf(Angle(8)))"
] | [
"Equals(MeasureOf(Angle(L, B, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(D, B, F)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, F, M)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(G, B, L)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(M, F, T)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"BD",
"BG",
"BJ",
"BL",
"BT",
"CE",
"DG",
"FB",
"FI",
"FJ",
"FL",
"FM",
"FT",
"IM",
"JC",
"JE",
"JL",
"TJ",
"TL"
] | {"B": [56.0, 114.0], "C": [296.0, 243.0], "D": [57.0, 1.0], "E": [296.0, 39.0], "F": [207.0, 150.0], "G": [57.0, 208.0], "I": [208.0, 225.0], "J": [297.0, 172.0], "L": [0.0, 101.0], "M": [208.0, 19.0], "T": [366.0, 188.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Arc(C, Y)), 3x-3)
- Equals(MeasureOf(Angle(B, P, Y)), 3x)
- Equals(MeasureOf(Arc(A, C)), 2x+15)
- PointLiesOnLine(P, Line(Y, X))
- PointLiesOnLine(P, Line(B, A))
- PointLiesOnCircle(Y, Circle(P, radius_1_0))
- PointLiesOnCircle(B, Circle(P, radius_1_0))
- PointLiesOnCircle(X, Circ... | 60 | [
"Find(MeasureOf(Arc(Y,C)))"
] | [
"Equals(MeasureOf(Arc(C, Y)), 3x-3)",
"Equals(MeasureOf(Angle(B, P, Y)), 3x)",
"Equals(MeasureOf(Arc(A, C)), 2x+15)",
"PointLiesOnLine(P, Line(Y, X))",
"PointLiesOnLine(P, Line(B, A))",
"PointLiesOnCircle(Y, Circle(P, radius_1_0))",
"PointLiesOnCircle(B, Circle(P, radius_1_0))",
"PointLiesOnCircle(X, ... | [
"BA",
"PA",
"PB",
"PC",
"PX",
"YP",
"YX"
] | {"A": [147.0, 168.0], "B": [37.0, 16.0], "C": [186.0, 88.0], "P": [92.0, 92.0], "X": [51.0, 176.0], "Y": [136.0, 9.0]} | [
"P"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 3)
- Equals(MeasureOf(Angle(A, N, B)), 62)
- Equals(LengthOf(Line(A, B)), LengthOf(Line(D, N)))
- Equals(LengthOf(Line(A, D)), LengthOf(Line(B, N)))
- Perpendicular(Line(A, D), Line(N, D))
- Perpendicular(Line(A, B), Line(B, N))
-
Find the perimeter of the figure. Ro... | 9.2 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, B)), 3)",
"Equals(MeasureOf(Angle(A, N, B)), 62)",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(D, N)))",
"Equals(LengthOf(Line(A, D)), LengthOf(Line(B, N)))",
"Perpendicular(Line(A, D), Line(N, D))",
"Perpendicular(Line(A, B), Line(B, N))",
""
] | [
"AB",
"BN",
"ND",
"AD",
"AN"
] | {"A": [10.0, 10.0], "B": [348.0, 12.0], "E": [349.0, 32.0], "N": [350.0, 192.0]} | [
""
] |
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(LengthOf(Line(B, A)), LengthOf(c))
- Equals(LengthOf(Line(B, C)), LengthOf(a))
- Equals(LengthOf(Line(A, C)), LengthOf(b))
- Perpendicular(Line(B, C), Line(A, C))
$a=14, b=48,$ and $c=50$ find $tanA$ | 0.29 | [
"Equals(a,14)",
"Equals(b,48)",
"Equals(c,50)",
"Find(TanOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(B, A)), LengthOf(c))",
"Equals(LengthOf(Line(B, C)), LengthOf(a))",
"Equals(LengthOf(Line(A, C)), LengthOf(b))",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"BA",
"BC",
"AC"
] | {"B": [0.0, 4.0], "A": [162.0, 90.0], "C": [0.9878021062201725, 87.99977271005379]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, Q)), 2)
- Equals(LengthOf(Line(P, Q)), 12)
- Equals(LengthOf(Line(T, S)), 3)
- PointLiesOnLine(Q, Line(P, R))
- PointLiesOnCircle(P, Circle(A, radius_2_0))
- PointLiesOnCircle(S, Circle(A, radius_2_0))
- PointLiesOnCircle(Q, Circle(A, radius_2_0))
- PointLiesOnCircle(T, Cir... | 4 | [
"Equals(LengthOf(Line(P,Q)),12)",
"Equals(LengthOf(Line(Q,R)),2)",
"Equals(LengthOf(Line(T,S)),3)",
"Find(LengthOf(Line(R,S)))"
] | [
"Equals(LengthOf(Line(R, Q)), 2)",
"Equals(LengthOf(Line(P, Q)), 12)",
"Equals(LengthOf(Line(T, S)), 3)",
"PointLiesOnLine(Q, Line(P, R))",
"PointLiesOnCircle(P, Circle(A, radius_2_0))",
"PointLiesOnCircle(S, Circle(A, radius_2_0))",
"PointLiesOnCircle(Q, Circle(A, radius_2_0))",
"PointLiesOnCircle(T,... | [
"QS",
"PQ",
"PR",
"RQ",
"RS"
] | {"A": [89.0, 87.0], "Q": [173.0, 69.0], "P": [3.0, 66.0], "R": [201.0, 68.0], "S": [170.0, 110.0], "T": [140.0, 152.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, K)), 2b+3)
- Equals(LengthOf(Line(J, M)), 3a)
- Equals(LengthOf(Line(L, K)), 21)
- Equals(MeasureOf(Angle(R, L, K)), 70)
- Equals(MeasureOf(Angle(M, L, J)), 30)
- Equals(LengthOf(Line(L, M)), 45)
- PointLiesOnLine(R, Line(L, J))
- PointLiesOnLine(R, Line(M, K))
Use paralle... | 80 | [
"Parallelogram(J,K,L,M)",
"Equals(LengthOf(Line(J,K)),2b+3)",
"Equals(LengthOf(Line(J,M)),3a)",
"Find(MeasureOf(Angle(J,M,L)))"
] | [
"Equals(LengthOf(Line(J, K)), 2b+3)",
"Equals(LengthOf(Line(J, M)), 3a)",
"Equals(LengthOf(Line(L, K)), 21)",
"Equals(MeasureOf(Angle(R, L, K)), 70)",
"Equals(MeasureOf(Angle(M, L, J)), 30)",
"Equals(LengthOf(Line(L, M)), 45)",
"PointLiesOnLine(R, Line(L, J))",
"PointLiesOnLine(R, Line(M, K))"
] | [
"JK",
"JM",
"JR",
"KR",
"LJ",
"LK",
"LM",
"LR",
"MK",
"MR"
] | {"J": [25.0, 1.0], "K": [299.0, 0.0], "L": [274.0, 144.0], "M": [1.0, 143.0], "R": [150.0, 72.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(C, E, B)), 110)
- Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(E, A, H)),... | 70 | [
"Find(MeasureOf(Angle(7)))"
] | [
"Equals(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(C, E, B)), 110)",
"Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(E, A, H)), M... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AH",
"AI",
"AK",
"AL",
"AM",
"BD",
"BI",
"BK",
"BL",
"CE",
"CF",
"DI",
"DK",
"DL",
"EB",
"ED",
"EI",
"EK",
"EL",
"FJ",
"GD",
"GH",
"GM",
"HJ",
"HM",
"IK",
"IL",
"JM",
"KL",
"NA",
"NC",
"NE",
"NF",
"NG"... | {"A": [133.0, 186.0], "B": [476.0, 63.0], "C": [219.0, 0.0], "D": [23.0, 230.0], "E": [325.0, 120.0], "F": [73.0, 313.0], "G": [47.0, 155.0], "H": [531.0, 326.0], "I": [519.0, 49.0], "J": [556.0, 315.0], "K": [498.0, 57.0], "L": [3.0, 233.0], "M": [551.0, 339.0], "N": [484.0, 314.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 3x+2)
- Equals(LengthOf(Line(T, R)), 2x+4)
- Equals(LengthOf(Line(S, R)), LengthOf(Line(R, T)))
Find $RS$. | 8 | [
"Find(LengthOf(Line(R,T)))"
] | [
"Equals(LengthOf(Line(R, S)), 3x+2)",
"Equals(LengthOf(Line(T, R)), 2x+4)",
"Equals(LengthOf(Line(S, R)), LengthOf(Line(R, T)))"
] | [
"RS",
"TR",
"TS"
] | {"R": [3.0, 0.0], "S": [387.0, 0.0], "T": [330.0, 192.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 8)
- Equals(LengthOf(Line(A, E)), 4)
- Equals(MeasureOf(Angle(C, F, E)), 60)
- Equals(LengthOf(Line(F, C)), 10)
- PointLiesOnLine(E, Line(A, F))
- PointLiesOnCircle(A, Circle(E, radius_4_0))
- PointLiesOnCircle(F, Circle(E, radius_4_0))
- PointLiesOnCircle(G, Circle(E,... | 87.5 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, E)), 4)",
"Equals(MeasureOf(Angle(C, F, E)), 60)",
"Equals(LengthOf(Line(F, C)), 10)",
"PointLiesOnLine(E, Line(A, F))",
"PointLiesOnCircle(A, Circle(E, radius_4_0))",
"PointLiesOnCircle(F, Circle(E, radius_4_0))",
"PointLiesOnCircle(G, Circl... | [
"AD",
"CD",
"CF",
"AF",
"AE",
"EF"
] | {"A": [155.0, 10.0], "C": [40.0, 142.0], "D": [1.0, 10.0], "E": [194.0, 73.0], "F": [230.0, 143.0]} | [
"E"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(MeasureOf(Angle(C, B, A)), 73)
- Equals(MeasureOf(Angle(A, C, B)), 67)
Find x. Round side measures to the nearest tenth. | 7.7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(MeasureOf(Angle(C, B, A)), 73)",
"Equals(MeasureOf(Angle(A, C, B)), 67)"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.3815288415768805, 0.9001471288242584], "B": [169.26830206830206, 133.61510341510342], "C": [47.06004100361223, 219.62419863972144]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(A, B)), 75)
- Equals(LengthOf(Line(B, C)), 40)
- Perpendicular(Line(A, B), Line(B, C))
Find x. | 85 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, B)), 75)",
"Equals(LengthOf(Line(B, C)), 40)",
"Perpendicular(Line(A, B), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [151.0, 1.0000000000000142], "B": [149.6771662790971, 187.0130364315411], "C": [0.0, 189.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, E)), 5)
- Equals(LengthOf(Line(C, G)), 2)
- Equals(LengthOf(Line(A, G)), 5)
- Equals(LengthOf(Line(C, F)), 6)
- Equals(LengthOf(Line(G, F)), 6)
- Equals(LengthOf(Line(D, B)), 1)
- Equals(LengthOf(Line(D, B)), 8)
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLine(H, Line(A, ... | 63.2 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(C, E)), 5)",
"Equals(LengthOf(Line(C, G)), 2)",
"Equals(LengthOf(Line(A, G)), 5)",
"Equals(LengthOf(Line(C, F)), 6)",
"Equals(LengthOf(Line(G, F)), 6)",
"Equals(LengthOf(Line(D, B)), 1)",
"Equals(LengthOf(Line(D, B)), 8)",
"PointLiesOnLine(G, Line(A, C))",
"PointLiesOnLine(H, L... | [
"AC",
"AD",
"AE",
"AG",
"AH",
"CE",
"CF",
"CG",
"DB",
"EB",
"EG",
"EH",
"GF",
"GH"
] | {"A": [257.5, 1.0], "B": [43.65246338215712, 127.00372836218375], "C": [108.00382186773014, 0.018112329677634875], "D": [214.57515815735542, 127.66042947518488], "E": [0.23109243697477666, 1.3291316526610686], "F": [130.0, 109.0], "G": [153.90294957183636, 1.4367269267364406], "H": [139.0, 2.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, A)), x)
- Equals(MeasureOf(Angle(A, C, B)), 2x)
- PointLiesOnLine(C, Line(B, D))
Find x | 60 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, C, A)), x)",
"Equals(MeasureOf(Angle(A, C, B)), 2x)",
"PointLiesOnLine(C, Line(B, D))"
] | [
"AC",
"CB",
"CD",
"BD"
] | {"A": [128.0, 1.0], "B": [200.0, 153.0], "C": [119.04858566612927, 96.48175289462114], "D": [0.0, 12.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, D, A)), b)
- Equals(MeasureOf(Angle(F, E, C)), d)
- PointLiesOnLine(D, Line(A, H))
- PointLiesOnLine(E, Line(D, C))
- PointLiesOnLine(E, Line(H, F))
- PointLiesOnLine(D, Line(C, G))
- PointLiesOnLine(E, Line(C, G))
- PointLiesOnLine(D, Line(E, G))
Which of the following ... | a + b = 90 | [
"Shape($)"
] | [
"Equals(MeasureOf(Angle(G, D, A)), b)",
"Equals(MeasureOf(Angle(F, E, C)), d)",
"PointLiesOnLine(D, Line(A, H))",
"PointLiesOnLine(E, Line(D, C))",
"PointLiesOnLine(E, Line(H, F))",
"PointLiesOnLine(D, Line(C, G))",
"PointLiesOnLine(E, Line(C, G))",
"PointLiesOnLine(D, Line(E, G))"
] | [
"AD",
"AH",
"CE",
"CG",
"DC",
"DE",
"DG",
"DH",
"EF",
"EG",
"HE",
"HF"
] | {"A": [18.0, 0.0], "C": [310.0, 66.0], "D": [85.0, 65.0], "E": [231.0, 66.0], "F": [296.0, 1.0], "G": [0.0, 65.0], "H": [158.0, 139.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, J, P)), 57)
- Equals(MeasureOf(Angle(J, H, L)), x)
- PointLiesOnLine(J, Line(K, L))
- PointLiesOnLine(P, Line(K, M))
- PointLiesOnLine(H, Line(L, M))
$\overline{JH}, \overline{JP},$ and $\overline{PH}$ are midsegments of $\triangle KLM$. Find $x$. | 57 | [
"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(H, J, P)), 57)",
"Equals(MeasureOf(Angle(J, H, L)), x)",
"PointLiesOnLine(J, Line(K, L))",
"PointLiesOnLine(P, Line(K, M))",
"PointLiesOnLine(H, Line(L, M))"
] | [
"KP",
"KL",
"KJ",
"KM",
"PH",
"PJ",
"PM",
"LH",
"LJ",
"LM",
"JH",
"MH"
] | {"K": [0.0, 0.0], "H": [336.49811589285935, 152.07414194864452], "P": [167.34003646291768, 140.99639275276024], "L": [386.4446723412983, 5.3195911530441435], "J": [203.46265775782422, 3.4775206443488003], "M": [301.407456998661, 253.7819892196244]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(P, L, Q)), 26)
- Equals(LengthOf(Line(J, P)), 20)
- Equals(MeasureOf(Angle(M, K, Q)), 29)
- Equals(LengthOf(Line(J, Q)), 25)
- PointLiesOnLine(N, Line(J, K))
- PointLiesOnLine(P, Line(J, L))
- PointLiesOnLine(M, Line(K, L))
- Perpendicular(Line(P, L), Line(P, Q))
- Perpendic... | 35 | [
"IsIncenterOf(Point(Q),Triangle(J,K,L))",
"Find(MeasureOf(Angle(Q,J,K)))"
] | [
"Equals(MeasureOf(Angle(P, L, Q)), 26)",
"Equals(LengthOf(Line(J, P)), 20)",
"Equals(MeasureOf(Angle(M, K, Q)), 29)",
"Equals(LengthOf(Line(J, Q)), 25)",
"PointLiesOnLine(N, Line(J, K))",
"PointLiesOnLine(P, Line(J, L))",
"PointLiesOnLine(M, Line(K, L))",
"Perpendicular(Line(P, L), Line(P, Q))",
"Pe... | [
"QK",
"QL",
"QM",
"QN",
"QP",
"JQ",
"JK",
"JL",
"JN",
"JP",
"KL",
"KM",
"KN",
"ML",
"PL"
] | {"J": [1.0, 318.0], "K": [374.0, 311.0], "L": [260.0, 1.0], "M": [325.0, 174.0], "N": [229.0, 314.0], "P": [143.0, 144.0], "Q": [224.0, 209.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(T, E))
- PointLiesOnLine(S, Line(R, K))
- PointLiesOnCircle(T, Circle(S, radius_0_0))
- PointLiesOnCircle(E, Circle(S, radius_0_0))
- PointLiesOnCircle(R, Circle(S, radius_0_0))
- PointLiesOnCircle(K, Circle(S, radius_0_0))
In $\odot S, m \angle T S R=42$
Find $m\widehat{... | 138 | [
"Circle(S)",
"Equals(MeasureOf(Angle(T,S,R)),42)",
"Find(MeasureOf(Arc(K,T)))"
] | [
"PointLiesOnLine(S, Line(T, E))",
"PointLiesOnLine(S, Line(R, K))",
"PointLiesOnCircle(T, Circle(S, radius_0_0))",
"PointLiesOnCircle(E, Circle(S, radius_0_0))",
"PointLiesOnCircle(R, Circle(S, radius_0_0))",
"PointLiesOnCircle(K, Circle(S, radius_0_0))"
] | [
"SE",
"SK",
"SR",
"ST",
"EK",
"RK",
"TE",
"TR"
] | {"S": [90.0, 90.0], "E": [115.0, 175.0], "K": [62.0, 174.0], "R": [119.0, 2.0], "T": [61.0, 2.0]} | [
"S"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, D, E)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, D, G)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(D, E, F)), 25)
- Equals(MeasureOf(Angle(E, F, D)), 65)
- PointLiesOnLine(G, Line(E, F))
- Perpendicular(Line(D, G), Line(E, G))
Find the measure of $\angle 2$. | 25 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(G, D, E)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, D, G)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(D, E, F)), 25)",
"Equals(MeasureOf(Angle(E, F, D)), 65)",
"PointLiesOnLine(G, Line(E, F))",
"Perpendicular(Line(D, G), Line(E, G))"
] | [
"DF",
"DG",
"ED",
"EF",
"EG",
"FG"
] | {"D": [402.0, 0.0], "E": [1.0, 189.0], "F": [489.0, 189.0], "G": [404.0, 189.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, B, A)), 4z+2)
- Equals(MeasureOf(Angle(J, B, L)), x)
- Equals(MeasureOf(Angle(J, B, A)), 3y-11)
- Equals(MeasureOf(Angle(E, A, B)), y+19)
- PointLiesOnLine(B, Line(L, E))
- PointLiesOnLine(A, Line(E, I))
- PointLiesOnLine(B, Line(F, H))
- Perpendicular(Line(E, B), Line(A,... | 15 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(E, B, A)), 4z+2)",
"Equals(MeasureOf(Angle(J, B, L)), x)",
"Equals(MeasureOf(Angle(J, B, A)), 3y-11)",
"Equals(MeasureOf(Angle(E, A, B)), y+19)",
"PointLiesOnLine(B, Line(L, E))",
"PointLiesOnLine(A, Line(E, I))",
"PointLiesOnLine(B, Line(F, H))",
"Perpendicular(Line(E, B), Lin... | [
"AH",
"AI",
"BA",
"BE",
"BG",
"BH",
"BJ",
"EA",
"EG",
"EI",
"FA",
"FB",
"FH",
"LB",
"LE",
"LG",
"MB",
"MJ"
] | {"A": [206.0, 133.0], "B": [77.0, 49.0], "C": [77.0, 195.0], "D": [205.0, 194.0], "E": [206.0, 49.0], "F": [0.0, 0.0], "G": [284.0, 50.0], "H": [284.0, 183.0], "I": [204.0, 242.0], "J": [76.0, 240.0], "K": [123.0, 56.0], "L": [0.0, 49.0], "M": [77.0, 2.0], "N": [103.0, 57.0]} | [
""
] |
Quadrilateral ABCD is a rhombus. If $m\angle BCD$ = 64, find $m\angle BAC$. | 32 | [
"Rhombus(A,B,C,D)",
"Equals(MeasureOf(Angle(B,C,D)),64)",
"Find(MeasureOf(Angle(B,A,C)))"
] | [] | [
"CB",
"CA",
"CD",
"BA",
"AD"
] | {"C": [101.83751543697312, 112.30685268111216], "B": [135.2342892697551, 0.6625091916963584], "A": [33.66764504871083, 0.0064196639299112235], "D": [0.20001131285705753, 111.6685898523672]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, F)), 1.3)
- Equals(MeasureOf(Angle(F, G, H)), 99)
- PointLiesOnCircle(H, Circle(G, radius_1_0))
- PointLiesOnCircle(F, Circle(G, radius_1_0))
Find the area of the shaded sector. Round to the nearest tenth. | 1.5 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(G, F)), 1.3)",
"Equals(MeasureOf(Angle(F, G, H)), 99)",
"PointLiesOnCircle(H, Circle(G, radius_1_0))",
"PointLiesOnCircle(F, Circle(G, radius_1_0))"
] | [
"GF",
"HG"
] | {"F": [86.0, 1.0], "G": [82.0, 85.0], "H": [163.0, 97.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, H)), 17)
- Equals(LengthOf(Line(G, F)), 9x-6)
- Equals(LengthOf(Line(G, H)), 7x+4)
- Equals(LengthOf(Line(G, F)), LengthOf(Line(G, H)))
Find $GH$ | 39 | [
"Find(LengthOf(Line(F,G)))"
] | [
"Equals(LengthOf(Line(F, H)), 17)",
"Equals(LengthOf(Line(G, F)), 9x-6)",
"Equals(LengthOf(Line(G, H)), 7x+4)",
"Equals(LengthOf(Line(G, F)), LengthOf(Line(G, H)))"
] | [
"FH",
"GF",
"GH"
] | {"F": [2.0, 2.0], "G": [106.0, 158.0], "H": [281.0, 158.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 10)
- Equals(LengthOf(Line(C, B)), 2x+4)
- Equals(LengthOf(Line(D, B)), x+2)
- Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))
Find $x$. | 3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(C, B)), 2x+4)",
"Equals(LengthOf(Line(D, B)), x+2)",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(C, D)))"
] | [
"CB",
"CD",
"DB"
] | {"B": [2.0, 135.0], "C": [269.0, 0.0], "D": [536.0, 136.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(M, Line(L, J))
In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=58$, find $m \angle PJL$. | 30.5 | [
"Equals(LengthOf(Line(J,M)),Line(P,M))",
"Equals(LengthOf(Line(M,L)),Line(P,L))",
"Equals(MeasureOf(Angle(P,L,J)),58)",
"Find(MeasureOf(Angle(P,J,L)))"
] | [
"PointLiesOnLine(M, Line(L, J))"
] | [
"JM",
"LJ",
"LM",
"PJ",
"PL",
"PM"
] | {"J": [1.0, 82.0], "L": [226.0, 82.0], "M": [67.0, 82.0], "P": [84.0, 3.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, D, C)), MeasureOf(Angle(3)))
- Equals(MeasureOf(Angle(A, B, C)), 32)
- PointLiesOnLine(E, Line(A, D))
- PointLiesOnLine(E, Line(B, C))
- PointLiesOnLine(H, Line(B, C))
- PointLiesOnLine(E, Line(B, H))
- PointLiesOnLine(H, Line(E, C))
- PointLiesOnCircle(A, Circle(H, radiu... | 32 | [
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(E, D, C)), MeasureOf(Angle(3)))",
"Equals(MeasureOf(Angle(A, B, C)), 32)",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(E, Line(B, C))",
"PointLiesOnLine(H, Line(B, C))",
"PointLiesOnLine(E, Line(B, H))",
"PointLiesOnLine(H, Line(E, C))",
"PointLiesOnCircle(A, Circle(H, r... | [
"AB",
"AD",
"AE",
"BC",
"BE",
"BH",
"CH",
"DC",
"DE",
"EC",
"EH"
] | {"A": [19.0, 27.0], "B": [61.0, 149.0], "C": [98.0, 3.0], "D": [114.0, 142.0], "E": [75.0, 94.0], "F": [23.0, 126.0], "H": [80.0, 76.0]} | [
"H"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, C, P)), 108)
- Equals(MeasureOf(Angle(N, C, R)), 62)
- Equals(MeasureOf(Angle(N, M, R)), x)
- PointLiesOnLine(N, Line(P, M))
- PointLiesOnCircle(N, Circle(C, radius_6_0))
- PointLiesOnCircle(P, Circle(C, radius_6_0))
- PointLiesOnCircle(R, Circle(C, radius_6_0))
What is ... | 64 | [
"Equals(MeasureOf(Arc(N,R)),62)",
"Equals(MeasureOf(Arc(N,P)),108)",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(N, C, P)), 108)",
"Equals(MeasureOf(Angle(N, C, R)), 62)",
"Equals(MeasureOf(Angle(N, M, R)), x)",
"PointLiesOnLine(N, Line(P, M))",
"PointLiesOnCircle(N, Circle(C, radius_6_0))",
"PointLiesOnCircle(P, Circle(C, radius_6_0))",
"PointLiesOnCircle(R, Circle(C, radius_6_0))"
] | [
"MR",
"NM",
"NP",
"PM"
] | {"C": [287.0, 134.0], "M": [2.0, 184.0], "N": [155.0, 144.0], "P": [410.0, 79.0], "R": [247.0, 260.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, E, A)), 45)
- Equals(LengthOf(Line(A, G)), x)
- Equals(LengthOf(Line(A, E)), 8)
- Equals(LengthOf(Line(G, D)), y)
- Equals(MeasureOf(Angle(A, D, E)), 30)
- PointLiesOnLine(G, Line(D, E))
- Perpendicular(Line(G, A), Line(G, D))
Find y. | 4 \sqrt { 6 } | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(D, E, A)), 45)",
"Equals(LengthOf(Line(A, G)), x)",
"Equals(LengthOf(Line(A, E)), 8)",
"Equals(LengthOf(Line(G, D)), y)",
"Equals(MeasureOf(Angle(A, D, E)), 30)",
"PointLiesOnLine(G, Line(D, E))",
"Perpendicular(Line(G, A), Line(G, D))"
] | [
"AD",
"AE",
"AG",
"ED",
"EG",
"GD"
] | {"A": [51.0, 190.0], "D": [315.0, 191.0], "E": [0.0, 0.0], "G": [120.0, 73.0]} | [
""
] |
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 $m\angle E$ | 158 | [
"Find(MeasureOf(Angle(E)))"
] | [
"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, B)), 18)
- Equals(LengthOf(Line(E, F)), x)
- Equals(AreaOf(Kite(E,F,G,H)), 525)
- Equals(AreaOf(Kite(A,B,X,C)), 1575)
For the pair of similar figures, use the given areas to find the scale factor from the blue to the green figure. | \frac { 1 } { \sqrt { 3 } } | [
"Similar(Shape($1),Shape($2))",
"Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))"
] | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(E, F)), x)",
"Equals(AreaOf(Kite(E,F,G,H)), 525)",
"Equals(AreaOf(Kite(A,B,X,C)), 1575)"
] | [
"AB",
"AC",
"BX",
"CX"
] | {"A": [257.0, 61.0], "B": [89.0, 106.0], "C": [90.0, 1.0], "X": [1.0, 51.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), 13)
- Equals(MeasureOf(Angle(C, E, A)), 18)
- Equals(MeasureOf(Angle(E, A, C)), 141)
- Equals(LengthOf(Line(C, E)), x)
Find x. Round the side measure to the nearest tenth. | 22.8 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, E)), 13)",
"Equals(MeasureOf(Angle(C, E, A)), 18)",
"Equals(MeasureOf(Angle(E, A, C)), 141)",
"Equals(LengthOf(Line(C, E)), x)"
] | [
"AC",
"AE",
"CE"
] | {"A": [146.0, 93.0], "C": [188.0, 228.0], "E": [1.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 34)
- Equals(MeasureOf(Angle(C, B, A)), 31)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, C), Line(B, C))
Find x | 29.1 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 34)",
"Equals(MeasureOf(Angle(C, B, A)), 31)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.6666666666666643, 0.18023255813952943], "B": [172.31500617404305, 93.68388899720543], "C": [0.6666666666666643, 92.00584795321637]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, E)), x)
- Equals(LengthOf(Line(B, E)), 2)
- Equals(LengthOf(Line(B, C)), 4)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnCircle(A, Circle(D, radius_3_0))
- PointLiesOnCircle(C, Circle(D, radius_3_0))
- PointLiesOnCircle(E, Circle(D, radius_3_0))
Find $x$ to the nearest te... | 6 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, E)), x)",
"Equals(LengthOf(Line(B, E)), 2)",
"Equals(LengthOf(Line(B, C)), 4)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(C, Circle(D, radius_3_0))",
"PointLiesOnCircle(E, Circle(D, radius_3_0))"
] | [
"AB",
"AE",
"BC",
"BE"
] | {"A": [156.0, 24.0], "B": [204.0, 192.0], "C": [90.0, 193.0], "D": [97.0, 101.0], "E": [186.0, 132.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(W, T, Z)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(Z, W, T)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(X, W, Y)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(Z, T, Y)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(T, Y, Z)), 52)
- Equals(MeasureOf(Angle(Z, Y, X)), ... | 52 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(W, T, Z)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(Z, W, T)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(X, W, Y)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(Z, T, Y)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(T, Y, Z)), 52)",
"Equals(MeasureOf(Angle(Z, Y, X)), 38... | [
"TZ",
"WT",
"WZ",
"XW",
"XY",
"YT",
"YW",
"YZ"
] | {"T": [0.0, 0.0], "W": [412.0, 2.0], "X": [412.0, 321.0], "Y": [2.0, 321.0], "Z": [160.0, 198.0]} | [
""
] |
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 $XZ = 2c$ and $ZY = 6$, and $XY = 8$, find $WY$. | 10 | [
"Rectangle(W,X,Y,Z)",
"Equals(LengthOf(Line(X,Z)),2c)",
"Equals(LengthOf(Line(Z,Y)),6)",
"Equals(LengthOf(Line(X,Y)),8)",
"Find(LengthOf(Line(W,Y)))"
] | [
"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(LengthOf(Line(C, I)), 15)
- Equals(LengthOf(Line(C, A)), 10)
- Equals(MeasureOf(Angle(A, C, I)), 45)
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 50 | [
"Find(PerimeterOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(C, I)), 15)",
"Equals(LengthOf(Line(C, A)), 10)",
"Equals(MeasureOf(Angle(A, C, I)), 45)"
] | [
"AB",
"AC",
"BI",
"CI"
] | {"A": [248.0, 118.0], "B": [1.0, 117.0], "C": [367.0, 1.0], "I": [117.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, C, A)), 2x+2y)
- Equals(MeasureOf(Angle(A, D, B)), 4y+x)
- Equals(MeasureOf(Angle(C, A, D)), x+y)
Find $y$ so that the quadrilateral is a parallelogram. | 20 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(B, C, A)), 2x+2y)",
"Equals(MeasureOf(Angle(A, D, B)), 4y+x)",
"Equals(MeasureOf(Angle(C, A, D)), x+y)"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [1.0, 221.0], "B": [427.0, 1.0], "C": [92.0, 32.0], "D": [336.0, 190.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, D)), 25)
- Equals(MeasureOf(Angle(E, C, B)), x)
- Equals(MeasureOf(Angle(B, D, C)), 20)
- PointLiesOnLine(C, Line(D, E))
-
Find x | 45 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, B, D)), 25)",
"Equals(MeasureOf(Angle(E, C, B)), x)",
"Equals(MeasureOf(Angle(B, D, C)), 20)",
"PointLiesOnLine(C, Line(D, E))",
""
] | [
"BD",
"BC",
"EC",
"CD",
"ED"
] | {"B": [81.0, 1.0], "C": [137.0, 112.0], "D": [285.0, 161.0], "E": [0.0, 66.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 3)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Equals(LengthOf(Line(A, B)), h)
- Perpendicular(Line(B, C), Line(A, C))
Find $h$ in the triangle. | 3 \sqrt 2 | [
"Triangle($)",
"Find(h)"
] | [
"Equals(LengthOf(Line(A, C)), 3)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Equals(LengthOf(Line(A, B)), h)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [226.0, 113.0], "B": [1.0, 114.0], "C": [113.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(C, D, B)), 58)
- Equals(LengthOf(Line(B, D)), 6)
- PointLiesOnLine(A, Line(B, D))
- Perpendicular(Line(A, C), Line(A, B))
- Equals(LengthOf(Line(C, D)), LengthOf(Line(B, C)))
Find $x$. Round to the nearest tenth. | 4.8 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(C, D, B)), 58)",
"Equals(LengthOf(Line(B, D)), 6)",
"PointLiesOnLine(A, Line(B, D))",
"Perpendicular(Line(A, C), Line(A, B))",
"Equals(LengthOf(Line(C, D)), LengthOf(Line(B, C)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [108.0, 173.0], "B": [216.0, 172.0], "C": [108.0, 2.0], "D": [1.0, 173.0]} | [
""
] |
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 $DB$. | 9.2 | [
"Find(LengthOf(Line(D,B)))"
] | [
"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))"
] | [
"BA",
"BD",
"CA",
"CB",
"CF",
"DA",
"EB",
"EC",
"ED",
"EF",
"FA"
] | {"A": [226.0, 48.0], "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]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 3y-8)
- Equals(MeasureOf(Angle(F, B, A)), 20)
- Equals(LengthOf(Line(D, A)), 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(D, C)), 10)
- PointLiesOnLine(F, Line(D, B))
- P... | 72 | [
"Parallelogram(A,B,C,D)",
"Find(MeasureOf(Angle(D,A,C)))"
] | [
"Equals(LengthOf(Line(A, B)), 3y-8)",
"Equals(MeasureOf(Angle(F, B, A)), 20)",
"Equals(LengthOf(Line(D, A)), 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(D, C)), 10)",
"PointLiesOnLine(F, Line(D, B))... | [
"AB",
"AF",
"BF",
"CA",
"CB",
"CF",
"DA",
"DB",
"DC",
"DF"
] | {"A": [97.0, 1.0], "B": [392.0, 1.0], "C": [296.0, 239.0], "D": [1.0, 240.0], "F": [197.0, 120.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, A, C)), 4x+5)
- Equals(MeasureOf(Angle(A, D, B)), y^2-1)
- Equals(MeasureOf(Angle(B, A, C)), 9x+20)
- Equals(MeasureOf(Angle(C, B, D)), 4y+4)
- PointLiesOnLine(F, Line(B, D))
- PointLiesOnLine(H, Line(B, Y))
- PointLiesOnLine(F, Line(C, E))
- PointLiesOnLine(E, Line(C, A)... | 5 | [
"Rectangle(A,B,C,D)",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, A, C)), 4x+5)",
"Equals(MeasureOf(Angle(A, D, B)), y^2-1)",
"Equals(MeasureOf(Angle(B, A, C)), 9x+20)",
"Equals(MeasureOf(Angle(C, B, D)), 4y+4)",
"PointLiesOnLine(F, Line(B, D))",
"PointLiesOnLine(H, Line(B, Y))",
"PointLiesOnLine(F, Line(C, E))",
"PointLiesOnLine(E, Line(C... | [
"AE",
"AG",
"BA",
"BC",
"BD",
"BF",
"BH",
"BY",
"CA",
"CE",
"CF",
"CH",
"CY",
"DA",
"DC",
"DE",
"DF",
"DG",
"DH",
"EG",
"FA",
"FE",
"FH",
"YH"
] | {"A": [30.0, 5.0], "B": [30.0, 127.0], "C": [309.0, 127.0], "D": [308.0, 6.0], "E": [49.0, 15.0], "F": [170.0, 67.0], "G": [105.0, 10.0], "H": [58.0, 123.0], "Y": [101.0, 124.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 50)
- Equals(LengthOf(Line(A, C)), 14)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 48 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 50)",
"Equals(LengthOf(Line(A, C)), 14)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.13691343170160053, 40.653769024549845], "B": [414.0, 1.999999999999993], "C": [45.974711583478324, 150.2741476776443]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 2\sqrt{3})
- Equals(MeasureOf(Angle(B, A, C)), 30)
- Equals(LengthOf(Line(A, Y)), x)
- Equals(LengthOf(Line(C, Y)), y)
- Equals(MeasureOf(Angle(A, C, B)), 60)
- PointLiesOnLine(Y, Line(A, C))
- Perpendicular(Line(A, B), Line(B, C))
- Perpendicular(Line(Y, B), Line(A, Y... | 1 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, B)), 2\\sqrt{3})",
"Equals(MeasureOf(Angle(B, A, C)), 30)",
"Equals(LengthOf(Line(A, Y)), x)",
"Equals(LengthOf(Line(C, Y)), y)",
"Equals(MeasureOf(Angle(A, C, B)), 60)",
"PointLiesOnLine(Y, Line(A, C))",
"Perpendicular(Line(A, B), Line(B, C))",
"Perpendicular(Line(Y, B), Line... | [
"AB",
"AC",
"AY",
"BC",
"YB",
"YC"
] | {"A": [0.0, 0.0], "B": [292.0, 1.0], "C": [293.0, 168.0], "Y": [219.0, 126.0]} | [
""
] |
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(... | 40 | [
"Circle(X)",
"Equals(LengthOf(Line(A,B)),30)",
"Equals(LengthOf(Line(C,D)),30)",
"Equals(MeasureOf(Arc(C,Z)),40)",
"Find(MeasureOf(Arc(D,Z)))"
] | [
"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(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(C, E, B)), 110)
- Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))
- Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(E, A, H)),... | 65 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(N, C, A)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(C, E, B)), 110)",
"Equals(MeasureOf(Angle(A, E, C)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(C, A, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Angle(N, E, D)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(E, A, H)), M... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AH",
"AI",
"AK",
"AL",
"AM",
"BD",
"BI",
"BK",
"BL",
"CE",
"CF",
"DI",
"DK",
"DL",
"EB",
"ED",
"EI",
"EK",
"EL",
"FJ",
"GD",
"GH",
"GM",
"HJ",
"HM",
"IK",
"IL",
"JM",
"KL",
"NA",
"NC",
"NE",
"NF",
"NG"... | {"A": [133.0, 186.0], "B": [476.0, 63.0], "C": [219.0, 0.0], "D": [23.0, 230.0], "E": [325.0, 120.0], "F": [73.0, 313.0], "G": [47.0, 155.0], "H": [531.0, 326.0], "I": [519.0, 49.0], "J": [556.0, 315.0], "K": [498.0, 57.0], "L": [3.0, 233.0], "M": [551.0, 339.0], "N": [484.0, 314.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 8.8)
- Equals(LengthOf(Line(A, D)), x)
- Equals(LengthOf(Line(A, B)), y)
- Equals(LengthOf(Line(B, C)), z)
- Equals(LengthOf(Line(B, D)), 8.5)
- PointLiesOnLine(A, Line(C, D))
- Perpendicular(Line(B, D), Line(B, C))
Refer to the figure at the right. Find z. | 11.09 | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, C)), 8.8)",
"Equals(LengthOf(Line(A, D)), x)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(LengthOf(Line(B, C)), z)",
"Equals(LengthOf(Line(B, D)), 8.5)",
"PointLiesOnLine(A, Line(C, D))",
"Perpendicular(Line(B, D), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [131.0, 10.0], "B": [137.0, 177.0], "C": [347.0, 1.0], "D": [1.0, 15.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), LengthOf(k))
- PointLiesOnLine(D, Line(A, C))
- PointLiesOnLine(M, Line(A, C))
- PointLiesOnLine(M, Line(A, D))
- PointLiesOnLine(N, Line(C, H))
- PointLiesOnLine(I, Line(C, B))
- PointLiesOnLine(D, Line(C, M))
- PointLiesOnLine(F, Line(E, D))
- PointLiesOnLine(A, Line... | 27.5 | [
"Tangent(Line(A,E),Circle($))",
"Equals(LengthOf(Line(A,D)),12)",
"Equals(LengthOf(Line(F,E)),18)",
"Find(LengthOf(Line(A,E)))"
] | [
"Equals(LengthOf(Line(D, B)), LengthOf(k))",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnLine(M, Line(A, C))",
"PointLiesOnLine(M, Line(A, D))",
"PointLiesOnLine(N, Line(C, H))",
"PointLiesOnLine(I, Line(C, B))",
"PointLiesOnLine(D, Line(C, M))",
"PointLiesOnLine(F, Line(E, D))",
"PointLiesOnLine(... | [
"AB",
"AC",
"AD",
"AE",
"AL",
"AM",
"BI",
"BL",
"CB",
"CD",
"CG",
"CH",
"CI",
"CK",
"CM",
"CN",
"DB",
"DF",
"DH",
"DI",
"DJ",
"DL",
"DM",
"DN",
"ED",
"EF",
"EL",
"EM",
"FG",
"FI",
"FJ",
"GH",
"GK",
"GN",
"HK",
"HN",
"IJ",
"KN",
"LH",
"MF"... | {"A": [99.0, 13.0], "B": [32.0, 15.0], "C": [28.0, 120.0], "D": [64.0, 65.0], "E": [197.0, 65.0], "F": [128.0, 65.0], "G": [127.0, 128.0], "H": [62.0, 130.0], "I": [31.0, 46.0], "J": [5.0, 41.0], "K": [85.0, 128.0], "L": [84.0, 3.0], "M": [71.0, 54.0], "N": [49.0, 128.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(V, U, T)), 3x-4)
- Equals(MeasureOf(Angle(W, V, U)), x)
- Equals(MeasureOf(Angle(T, W, V)), 3x-4)
- Equals(MeasureOf(Angle(U, T, W)), x)
Find $\angle V$ | 46 | [
"Find(MeasureOf(Angle(V)))"
] | [
"Equals(MeasureOf(Angle(V, U, T)), 3x-4)",
"Equals(MeasureOf(Angle(W, V, U)), x)",
"Equals(MeasureOf(Angle(T, W, V)), 3x-4)",
"Equals(MeasureOf(Angle(U, T, W)), x)"
] | [
"TW",
"TU",
"WV",
"UV"
] | {"T": [0.0, 113.0], "V": [356.9946018893387, 0.6720647773279325], "W": [245.66261808367074, 112.33738191632929], "U": [110.00892057464263, 1.9999283487980506]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, F, G)), x+20)
- Equals(MeasureOf(Angle(F, E, J)), x)
- Equals(MeasureOf(Angle(J, H, G)), x-5)
- Equals(MeasureOf(Angle(E, J, H)), x+10)
- Equals(MeasureOf(Angle(F, G, H)), x+5)
Find $m\angle J$ | 112 | [
"Find(MeasureOf(Angle(J)))"
] | [
"Equals(MeasureOf(Angle(E, F, G)), x+20)",
"Equals(MeasureOf(Angle(F, E, J)), x)",
"Equals(MeasureOf(Angle(J, H, G)), x-5)",
"Equals(MeasureOf(Angle(E, J, H)), x+10)",
"Equals(MeasureOf(Angle(F, G, H)), x+5)"
] | [
"EJ",
"FE",
"GF",
"GH",
"HJ"
] | {"E": [2.0, 54.0], "F": [31.0, 0.0], "G": [203.0, 2.0], "H": [233.0, 109.0], "J": [134.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, B)), x+5)
- Equals(LengthOf(Line(C, B)), 2y+5)
- Equals(LengthOf(Line(A, D)), y+10)
- Equals(LengthOf(Line(A, C)), 2x+2)
Find $y$ so that the quadrilateral is a parallelogram | 5 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(D, B)), x+5)",
"Equals(LengthOf(Line(C, B)), 2y+5)",
"Equals(LengthOf(Line(A, D)), y+10)",
"Equals(LengthOf(Line(A, C)), 2x+2)"
] | [
"AC",
"AD",
"CB",
"DB"
] | {"A": [0.0, 226.0], "B": [264.0, 1.0], "C": [263.0, 169.0], "D": [1.0, 59.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(A, D, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(G, C, B)), MeasureOf(angle 3))
- PointLiesOnLine(B, Line(G, A))
- PointLiesOnLine(F, Line(A, D))
- Perpendi... | 50 | [
"Equals(MeasureOf(Angle(D,G,F)),53)",
"Equals(MeasureOf(Angle(A,G,C)),40)",
"Find(MeasureOf(Angle(3)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, D, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(G, C, B)), MeasureOf(angle 3))",
"PointLiesOnLine(B, Line(G, A))",
"PointLiesOnLine(F, Line(A, D))",
"Perpend... | [
"AB",
"AC",
"AD",
"AF",
"CB",
"DF",
"GA",
"GB",
"GC",
"GD",
"GF"
] | {"A": [532.0, 1.0], "B": [426.0, 88.0], "C": [532.0, 212.0], "D": [0.0, 0.0], "F": [280.0, 0.0], "G": [282.0, 210.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, A, E)), 5y+5)
- Equals(MeasureOf(Angle(A, D, E)), 4z+9)
- Equals(MeasureOf(Angle(C, E, A)), 135)
- Equals(MeasureOf(Angle(A, D, F)), 9y-2)
- PointLiesOnLine(E, Line(D, C))
- PointLiesOnLine(B, Line(D, F))
- PointLiesOnLine(D, Line(E, B))
- PointLiesOnLine(B, Line(E, F))
-... | 13 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(D, A, E)), 5y+5)",
"Equals(MeasureOf(Angle(A, D, E)), 4z+9)",
"Equals(MeasureOf(Angle(C, E, A)), 135)",
"Equals(MeasureOf(Angle(A, D, F)), 9y-2)",
"PointLiesOnLine(E, Line(D, C))",
"PointLiesOnLine(B, Line(D, F))",
"PointLiesOnLine(D, Line(E, B))",
"PointLiesOnLine(B, Line(E, F... | [
"AD",
"AE",
"BC",
"BF",
"CF",
"DB",
"DC",
"DE",
"DF",
"EB",
"EC",
"EF"
] | {"A": [362.0, -0.0], "B": [677.0, 298.0], "C": [0.0, 295.0], "D": [496.0, 296.0], "E": [72.0, 296.0], "F": [704.0, 296.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(W, Y))
- PointLiesOnLine(T, Line(X, Z))
- Perpendicular(Line(W, X), Line(Y, X))
- Perpendicular(Line(W, X), Line(W, Z))
- Perpendicular(Line(Y, X), Line(Y, Z))
- Perpendicular(Line(W, Z), Line(Y, Z))
WXYZ is a square. If $WT = 3$, find $ZX$ | 6 | [
"Square(W,X,Y,Z)",
"Equals(LengthOf(Line(W,T)),3)",
"Find(LengthOf(Line(Z,X)))"
] | [
"PointLiesOnLine(T, Line(W, Y))",
"PointLiesOnLine(T, Line(X, Z))",
"Perpendicular(Line(W, X), Line(Y, X))",
"Perpendicular(Line(W, X), Line(W, Z))",
"Perpendicular(Line(Y, X), Line(Y, Z))",
"Perpendicular(Line(W, Z), Line(Y, Z))"
] | [
"WY",
"WX",
"WZ",
"WT",
"YX",
"YZ",
"YT",
"XZ",
"XT",
"ZT"
] | {"W": [142.6735959307499, 0.8218706793993817], "Y": [-1.4210854715202004e-14, 143.0], "X": [1.4896551724137765, 0.4931034482758747], "Z": [142.33333333333331, 143.0], "T": [71.74560800863676, 72.25085876926097]} | [] |
Diagram Logic Form:
- PointLiesOnLine(P, Line(Q, T))
- PointLiesOnLine(M, Line(R, S))
For trapezoid QRST, M and P are midpoints of the legs. If PM = 2x, QR = 3x, and TS = 10, find PM. | 20 | [
"Trapezoid(Q,R,S,T)",
"IsMidpointOf(Point(M),LegOf(Trapezoid(Q,R,S,T)))",
"IsMidpointOf(Point(P),LegOf(Trapezoid(Q,R,S,T)))",
"Equals(LengthOf(Line(P,M)),2x)",
"Equals(LengthOf(Line(Q,R)),3x)",
"Equals(LengthOf(Line(T,S)),10)",
"Find(LengthOf(Line(P,M)))"
] | [
"PointLiesOnLine(P, Line(Q, T))",
"PointLiesOnLine(M, Line(R, S))"
] | [
"MS",
"PM",
"QP",
"QR",
"QT",
"RM",
"RS",
"TP",
"TS"
] | {"M": [172.0, 68.0], "P": [25.0, 70.0], "Q": [0.0, 0.0], "R": [197.0, 1.0], "S": [145.0, 140.0], "T": [50.0, 139.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, D, E)), 12x+72)
- Equals(MeasureOf(Angle(D, E, A)), 3y+36)
- Equals(MeasureOf(Angle(C, A, E)), 25x+20)
- Equals(MeasureOf(Angle(A, C, D)), 9y-12)
Find $y$ so that the quadrilateral is a parallelogram. | 8 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(C, D, E)), 12x+72)",
"Equals(MeasureOf(Angle(D, E, A)), 3y+36)",
"Equals(MeasureOf(Angle(C, A, E)), 25x+20)",
"Equals(MeasureOf(Angle(A, C, D)), 9y-12)"
] | [
"AC",
"AE",
"CD",
"ED"
] | {"A": [353.0, 230.0], "C": [0.0, 231.0], "D": [118.0, 0.0], "E": [464.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, E)), 4)
- Equals(LengthOf(Line(E, F)), 3)
- PointLiesOnLine(C, Line(F, D))
- PointLiesOnCircle(E, Circle(F, radius_1_0))
- PointLiesOnCircle(C, Circle(F, radius_1_0))
$\overline{E D}$ is tangent to $\odot F$ at point $E .$ Find $x$ | 5 | [
"Tangent(Line(E,D),Circle(F)) at Point(E)",
"Find(x)"
] | [
"Equals(LengthOf(Line(D, E)), 4)",
"Equals(LengthOf(Line(E, F)), 3)",
"PointLiesOnLine(C, Line(F, D))",
"PointLiesOnCircle(E, Circle(F, radius_1_0))",
"PointLiesOnCircle(C, Circle(F, radius_1_0))"
] | [
"DC",
"ED",
"EF",
"FC",
"FD"
] | {"C": [73.0, 52.0], "D": [1.0, 37.0], "E": [119.0, 3.0], "F": [139.0, 66.0]} | [
"F"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, Q)), 3x+2)
- Equals(LengthOf(Line(Q, L)), 12)
- Equals(LengthOf(Line(N, M)), 2y+5)
- Equals(LengthOf(Line(R, Q)), 3y)
- Equals(LengthOf(Line(M, L)), LengthOf(w))
- Equals(LengthOf(Line(R, M)), 4x-2)
- PointLiesOnLine(L, Line(N, R))
- PointLiesOnLine(L, Line(Q, M))
Use para... | 14 | [
"Parallelogram(N,Q,R,M)",
"Find(LengthOf(Line(N,Q)))"
] | [
"Equals(LengthOf(Line(N, Q)), 3x+2)",
"Equals(LengthOf(Line(Q, L)), 12)",
"Equals(LengthOf(Line(N, M)), 2y+5)",
"Equals(LengthOf(Line(R, Q)), 3y)",
"Equals(LengthOf(Line(M, L)), LengthOf(w))",
"Equals(LengthOf(Line(R, M)), 4x-2)",
"PointLiesOnLine(L, Line(N, R))",
"PointLiesOnLine(L, Line(Q, M))"
] | [
"ML",
"NL",
"NM",
"NQ",
"NR",
"QL",
"QM",
"RL",
"RM",
"RQ"
] | {"L": [142.0, 82.0], "M": [0.0, 166.0], "N": [70.0, 2.0], "Q": [282.0, 0.0], "R": [212.0, 165.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Z, Line(Y, V))
- PointLiesOnLine(Z, Line(W, U))
- PointLiesOnCircle(V, Circle(Z, radius_1_0))
- PointLiesOnCircle(W, Circle(Z, radius_1_0))
- PointLiesOnCircle(Y, Circle(Z, radius_1_0))
- PointLiesOnCircle(U, Circle(Z, radius_1_0))
- PointLiesOnCircle(X, Circle(Z, radius_1_0))
In ... | 76 | [
"Circle(Z)",
"Equals(Angle(W,Z,X),Angle(X,Z,Y))",
"Equals(MeasureOf(Angle(V,Z,U)),4x)",
"Equals(MeasureOf(Angle(U,Z,Y)),2x+24)",
"IsDiameterOf(Line(V,Y),Circle($))",
"IsDiameterOf(Line(W,U),Circle($))",
"Find(MeasureOf(Arc(W,V)))"
] | [
"PointLiesOnLine(Z, Line(Y, V))",
"PointLiesOnLine(Z, Line(W, U))",
"PointLiesOnCircle(V, Circle(Z, radius_1_0))",
"PointLiesOnCircle(W, Circle(Z, radius_1_0))",
"PointLiesOnCircle(Y, Circle(Z, radius_1_0))",
"PointLiesOnCircle(U, Circle(Z, radius_1_0))",
"PointLiesOnCircle(X, Circle(Z, radius_1_0))"
] | [
"VY",
"VZ",
"WU",
"ZU",
"ZW",
"ZX",
"ZY"
] | {"U": [168.0, 88.0], "V": [66.0, 2.0], "W": [0.0, 83.0], "X": [33.0, 151.0], "Y": [107.0, 165.0], "Z": [84.0, 85.0]} | [
"Z"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 22)
- Equals(LengthOf(Line(C, B)), 15)
- Equals(LengthOf(Line(B, D)), 31)
- PointLiesOnLine(O, Line(A, D))
- Equals(LengthOf(Line(O, D)), LengthOf(Line(B, D)))
- Equals(LengthOf(Line(O, A)), LengthOf(Line(A, C)))
Find the area of the figure. Round to the nearest tenth... | 374.5 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, C)), 22)",
"Equals(LengthOf(Line(C, B)), 15)",
"Equals(LengthOf(Line(B, D)), 31)",
"PointLiesOnLine(O, Line(A, D))",
"Equals(LengthOf(Line(O, D)), LengthOf(Line(B, D)))",
"Equals(LengthOf(Line(O, A)), LengthOf(Line(A, C)))"
] | [
"AC",
"BD",
"CB",
"DO"
] | {"A": [313.0, 3.0], "B": [0.0, 96.0], "C": [96.0, 2.0], "D": [310.0, 94.0], "O": [297.0, 72.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, E, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, C, D)), 50)
- Equals(MeasureOf(Angle(G, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, G, A)), 120)
- Equals(MeasureOf(Angle(H, G, F)), MeasureOf(angle... | 52 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(G, E, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(E, A, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, C, D)), 50)",
"Equals(MeasureOf(Angle(G, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, G, A)), 120)",
"Equals(MeasureOf(Angle(H, G, F)), MeasureOf(angle 4... | [
"AB",
"AC",
"AD",
"AE",
"AG",
"AH",
"BC",
"BF",
"BG",
"BH",
"CD",
"CG",
"CH",
"DE",
"EF",
"EG",
"GF",
"GH"
] | {"A": [189.0, 107.0], "B": [446.0, 107.0], "C": [1.0, 107.0], "D": [99.0, 222.0], "E": [271.0, 2.0], "F": [396.0, 216.0], "G": [333.0, 108.0], "H": [507.0, 108.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, C, G)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(C, G, D)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(A, D, C)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(D, G, B)), MeasureOf(angle 5))
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 1))
- Equals(MeasureOf(A... | 104 | [
"Rectangle(A,B,D,C)",
"Equals(MeasureOf(Angle(1)),38)",
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(D, C, G)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(C, G, D)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(A, D, C)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(D, G, B)), MeasureOf(angle 5))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 1))",
"Equals(MeasureOf(Ang... | [
"AB",
"AC",
"AD",
"AG",
"BD",
"CB",
"CD",
"GB",
"GC",
"GD"
] | {"A": [0.0, 1.0], "B": [3.0, 185.0], "C": [451.0, 2.0], "D": [452.0, 186.0], "G": [227.0, 94.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, N)), 36)
- Equals(LengthOf(Line(A, L)), 27)
- Equals(LengthOf(Line(A, B)), 40)
- PointLiesOnLine(A, Line(B, L))
- Perpendicular(Line(N, L), Line(L, A))
Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. | 170 | [
"Find(PerimeterOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(L, N)), 36)",
"Equals(LengthOf(Line(A, L)), 27)",
"Equals(LengthOf(Line(A, B)), 40)",
"PointLiesOnLine(A, Line(B, L))",
"Perpendicular(Line(N, L), Line(L, A))"
] | [
"AB",
"AL",
"AN",
"BC",
"BL",
"NC",
"NL"
] | {"A": [95.0, 124.0], "B": [232.0, 123.0], "C": [137.0, 0.0], "L": [1.0, 124.0], "N": [1.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(U, V, W)), 3x-11)
- Equals(MeasureOf(Angle(V, U, Z)), x-8)
- Equals(MeasureOf(Angle(Y, W, V)), x+8)
- Equals(MeasureOf(Angle(U, Z, Y)), 2x+7)
- Equals(MeasureOf(Angle(Z, Y, W)), x)
Find $m\angle V$ | 193 | [
"Find(MeasureOf(Angle(V)))"
] | [
"Equals(MeasureOf(Angle(U, V, W)), 3x-11)",
"Equals(MeasureOf(Angle(V, U, Z)), x-8)",
"Equals(MeasureOf(Angle(Y, W, V)), x+8)",
"Equals(MeasureOf(Angle(U, Z, Y)), 2x+7)",
"Equals(MeasureOf(Angle(Z, Y, W)), x)"
] | [
"UV",
"VW",
"WY",
"YZ",
"ZU"
] | {"U": [1.0, 56.0], "V": [164.0, 1.0], "W": [330.0, 105.0], "Y": [328.0, 410.0], "Z": [53.0, 308.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, C, I)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(N, C, J)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(I, C, O)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(K, C, N)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(O, C, B)), MeasureOf(angle 6))
- Equals(MeasureOf(A... | 62 | [
"Equals(MeasureOf(Angle(11)),62)",
"Equals(MeasureOf(Angle(14)),38)",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(J, C, I)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(N, C, J)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(I, C, O)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(K, C, N)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(O, C, B)), MeasureOf(angle 6))",
"Equals(MeasureOf(Ang... | [
"BC",
"BF",
"BH",
"BJ",
"BK",
"BM",
"CF",
"CG",
"CI",
"CJ",
"CN",
"CO",
"FJ",
"GI",
"HK",
"HM",
"KC",
"KG",
"KI",
"KM",
"NO"
] | {"B": [288.0, 254.0], "C": [204.0, 128.0], "F": [369.0, 376.0], "G": [119.0, 380.0], "H": [434.0, 253.0], "I": [244.0, 4.0], "J": [151.0, 47.0], "K": [160.0, 255.0], "M": [0.0, 253.0], "N": [5.0, 128.0], "O": [429.0, 128.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, S)), x)
- Equals(LengthOf(Line(Q, T)), 20)
- Equals(LengthOf(Line(R, S)), 12)
- Equals(LengthOf(Line(P, T)), 16)
- PointLiesOnLine(R, Line(Q, P))
- PointLiesOnLine(S, Line(Q, T))
- Parallel(Line(R, S), Line(T, P))
Find $ST$. | 5 | [
"Find(LengthOf(Line(S,T)))"
] | [
"Equals(LengthOf(Line(Q, S)), x)",
"Equals(LengthOf(Line(Q, T)), 20)",
"Equals(LengthOf(Line(R, S)), 12)",
"Equals(LengthOf(Line(P, T)), 16)",
"PointLiesOnLine(R, Line(Q, P))",
"PointLiesOnLine(S, Line(Q, T))",
"Parallel(Line(R, S), Line(T, P))"
] | [
"QS",
"QT",
"ST",
"QR",
"RP",
"QP",
"RS",
"PT"
] | {"S": [230.0, 217.0], "P": [1.0, 338.0], "Q": [112.0, 57.0], "R": [49.0, 215.0], "T": [317.0, 338.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(H, G)), 2)
- Equals(LengthOf(Line(F, G)), 2.5)
- Equals(LengthOf(Line(F, H)), 4)
- Equals(LengthOf(Line(F, E)), 6)
- PointLiesOnLine(F, Line(E, H))
- PointLiesOnLine(D, Line(E, C))
- PointLiesOnLine(G, Line(H, C))
Find the perimeter of $\triangle D E F$ if $\triangle D E F ... | 12.75 | [
"Similar(Triangle(D,E,F),Triangle(G,F,H))",
"Find(PerimeterOf(Triangle(D,E,F)))"
] | [
"Equals(LengthOf(Line(H, G)), 2)",
"Equals(LengthOf(Line(F, G)), 2.5)",
"Equals(LengthOf(Line(F, H)), 4)",
"Equals(LengthOf(Line(F, E)), 6)",
"PointLiesOnLine(F, Line(E, H))",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(G, Line(H, C))"
] | [
"GC",
"DC",
"EC",
"ED",
"EH",
"FG",
"FD",
"FE",
"FH",
"HG",
"HC"
] | {"G": [200.0, 20.0], "C": [98.0, 1.0], "D": [61.0, 54.0], "E": [1.0, 139.0], "F": [152.0, 75.0], "H": [256.0, 32.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, Q)), 25)
- Equals(LengthOf(Line(R, T)), x)
- Equals(LengthOf(Line(R, S)), 10)
- Equals(LengthOf(Line(S, Q)), 5)
- PointLiesOnLine(T, Line(P, R))
- PointLiesOnLine(S, Line(Q, R))
- Perpendicular(Line(R, T), Line(R, S))
- Parallel(Line(P, Q), Line(T, S))
Find ST | \frac { 50 } { 3 } | [
"Find(LengthOf(Line(S,T)))"
] | [
"Equals(LengthOf(Line(P, Q)), 25)",
"Equals(LengthOf(Line(R, T)), x)",
"Equals(LengthOf(Line(R, S)), 10)",
"Equals(LengthOf(Line(S, Q)), 5)",
"PointLiesOnLine(T, Line(P, R))",
"PointLiesOnLine(S, Line(Q, R))",
"Perpendicular(Line(R, T), Line(R, S))",
"Parallel(Line(P, Q), Line(T, S))"
] | [
"PQ",
"PR",
"PT",
"RQ",
"RS",
"SQ",
"TR",
"TS"
] | {"P": [0.0, 0.0], "Q": [123.0, 167.0], "R": [2.0, 165.0], "S": [86.0, 167.0], "T": [1.0, 57.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(S, Y))
- PointLiesOnLine(A, Line(S, Y))
- PointLiesOnLine(T, Line(S, A))
- PointLiesOnLine(Q, Line(Y, R))
- PointLiesOnLine(A, Line(Y, T))
- PointLiesOnLine(Y, Line(R, X))
- PointLiesOnLine(Q, Line(R, X))
- PointLiesOnLine(V, Line(A, W))
- PointLiesOnLine(A, Line(Q, V))
- P... | 4 | [
"Similar(Triangle(S,R,Y),Triangle(W,X,Q))",
"Equals(Line(R,T),AltitudeOf(Triangle(S,R,Y)))",
"Equals(Line(X,V),AltitudeOf(Triangle(W,X,Q)))",
"Equals(LengthOf(Line(R,T)),5)",
"Equals(LengthOf(Line(R,Q)),4)",
"Equals(LengthOf(Line(Q,Y)),6)",
"Equals(LengthOf(Line(Y,X)),2)",
"Find(LengthOf(Line(X,V)))"
... | [
"PointLiesOnLine(T, Line(S, Y))",
"PointLiesOnLine(A, Line(S, Y))",
"PointLiesOnLine(T, Line(S, A))",
"PointLiesOnLine(Q, Line(Y, R))",
"PointLiesOnLine(A, Line(Y, T))",
"PointLiesOnLine(Y, Line(R, X))",
"PointLiesOnLine(Q, Line(R, X))",
"PointLiesOnLine(V, Line(A, W))",
"PointLiesOnLine(A, Line(Q, ... | [
"AQ",
"AV",
"AW",
"QV",
"QW",
"QX",
"RQ",
"RT",
"RX",
"SA",
"SR",
"ST",
"SY",
"TA",
"VW",
"XV",
"XW",
"YA",
"YQ",
"YR",
"YT",
"YX"
] | {"A": [322.0, 105.0], "Q": [389.0, 213.0], "R": [388.0, 320.0], "S": [0.0, 321.0], "T": [268.0, 141.0], "V": [293.0, 60.0], "W": [258.0, 1.0], "X": [389.0, 1.0], "Y": [389.0, 60.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(E, Line(C, A))
- PointLiesOnCircle(B, Circle(Z, radius_1_0))
- PointLiesOnCircle(C, Circle(Z, radius_1_0))
- PointLiesOnCircle(D, Circle(Z, radius_1_0))
- PointLiesOnCircle(A, Circle(Z, radius_1_0))
Quadrilateral $A B C D$ is inscribed in $\odot Z$... | 162 | [
"InscribedIn(Quadrilateral(A,B,C,D),Circle(Z))",
"Equals(MeasureOf(Angle(B,Z,A)),104)",
"Equals(MeasureOf(Arc(C,B)),94)",
"Parallel(Line(A,B),Line(D,C))",
"Find(MeasureOf(Arc(A,D,C)))"
] | [
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(E, Line(C, A))",
"PointLiesOnCircle(B, Circle(Z, radius_1_0))",
"PointLiesOnCircle(C, Circle(Z, radius_1_0))",
"PointLiesOnCircle(D, Circle(Z, radius_1_0))",
"PointLiesOnCircle(A, Circle(Z, radius_1_0))"
] | [
"BZ",
"BC",
"BD",
"BA",
"BE",
"ZA",
"ZE",
"CD",
"CA",
"CE",
"DA",
"DE",
"AE"
] | {"B": [44.58493795492737, 31.70111822210704], "Z": [121.16666666666667, 124.83333333333333], "C": [223.51753040525023, 52.0513502069235], "D": [229.59104473898762, 187.6426408523185], "A": [56.57399636317476, 227.22763700556607], "E": [155.39507417542848, 124.00028805991647]} | [
"Z"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, F, X)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(F, E, I)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(H, W, L)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(P, A, C)), MeasureOf(angle 4))
- PointLiesOnLine(G, Line(L, N))
- PointLiesOnLine(G, Line(L, F))
- PointLie... | 75 | [
"Equals(MeasureOf(Angle(1)),3x+40)",
"Equals(MeasureOf(Angle(2)),2(y-10))",
"Equals(MeasureOf(Angle(3)),2x+70)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(R, F, X)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(F, E, I)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(H, W, L)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(P, A, C)), MeasureOf(angle 4))",
"PointLiesOnLine(G, Line(L, N))",
"PointLiesOnLine(G, Line(L, F))",
"PointLi... | [
"EI",
"EO",
"FE",
"FN",
"FN",
"FO",
"GF",
"GH",
"GM",
"GM",
"HE",
"HI",
"LG",
"LG",
"LN",
"PE",
"PH",
"PI",
"QG",
"QH",
"QM",
"RE",
"RF",
"RO"
] | {"B": [188.0, 63.0], "C": [41.0, 125.0], "E": [243.0, 182.0], "F": [162.0, 95.0], "G": [95.0, 182.0], "H": [177.0, 270.0], "I": [324.0, 80.0], "J": [103.0, 171.0], "K": [107.0, 38.0], "L": [4.0, 302.0], "M": [248.0, 349.0], "N": [237.0, 1.0], "O": [321.0, 269.0], "P": [115.0, 349.0], "Q": [4.0, 85.0], "R": [74.0, 3.0],... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, F, I)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(A, L, C)), 35)
- Equals(MeasureOf(Angle(C, B, G)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(G, B, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(E, K, I)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(H, C, F)), ... | 55 | [
"Find(MeasureOf(Angle(5)))"
] | [
"Equals(MeasureOf(Angle(C, F, I)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(A, L, C)), 35)",
"Equals(MeasureOf(Angle(C, B, G)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(G, B, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(E, K, I)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(H, C, F)), Me... | [
"AB",
"AC",
"AF",
"AH",
"AI",
"AJ",
"AK",
"AL",
"BC",
"BD",
"BE",
"BF",
"BG",
"BI",
"BJ",
"BK",
"BL",
"CD",
"CE",
"CF",
"CG",
"CH",
"CK",
"CL",
"DE",
"DG",
"EG",
"FI",
"FK",
"FL",
"ID",
"IJ",
"IK",
"IL",
"JD",
"JK",
"JL",
"KD",
"KE",
"KL"... | {"A": [744.0, 22.0], "B": [413.0, 65.0], "C": [773.0, 255.0], "D": [1.0, 254.0], "E": [255.0, 255.0], "F": [906.0, 2.0], "G": [410.0, 247.0], "H": [761.0, 161.0], "I": [377.0, 80.0], "J": [357.0, 87.0], "K": [399.0, 69.0], "L": [424.0, 60.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, B)), 3y-6)
- Equals(LengthOf(Line(B, F)), 2y+4)
- Equals(LengthOf(Line(F, G)), \frac{1}{2}x+12)
- Equals(LengthOf(Line(D, G)), \frac{3}{2}x+8)
- PointLiesOnLine(G, Line(D, F))
- PointLiesOnLine(B, Line(E, F))
-
Find $y$. | 10 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(E, B)), 3y-6)",
"Equals(LengthOf(Line(B, F)), 2y+4)",
"Equals(LengthOf(Line(F, G)), \\frac{1}{2}x+12)",
"Equals(LengthOf(Line(D, G)), \\frac{3}{2}x+8)",
"PointLiesOnLine(G, Line(D, F))",
"PointLiesOnLine(B, Line(E, F))",
""
] | [
"BF",
"BG",
"DE",
"DF",
"DG",
"EB",
"EF",
"FG"
] | {"B": [133.0, 99.0], "D": [296.0, 328.0], "E": [261.0, 1.0], "F": [0.0, 196.0], "G": [153.0, 264.0]} | [
""
] |
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