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(MeasureOf(Angle(D, C, F)), 53)
- Equals(MeasureOf(Angle(E, C, B)), MeasureOf(Angle(2)))
- PointLiesOnLine(C, Line(B, F))
- PointLiesOnLine(C, Line(D, E))
Find the measure of $\angle 2$. | 53 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(D, C, F)), 53)",
"Equals(MeasureOf(Angle(E, C, B)), MeasureOf(Angle(2)))",
"PointLiesOnLine(C, Line(B, F))",
"PointLiesOnLine(C, Line(D, E))"
] | [
"BC",
"BF",
"CD",
"CE",
"CF",
"DE"
] | {"B": [284.0, 89.0], "C": [140.0, 55.0], "D": [62.0, 120.0], "E": [204.0, 1.0], "F": [1.0, 23.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(N, B, E)), 45)
- Equals(LengthOf(Line(A, N)), 12.8)
- Equals(LengthOf(Line(B, N)), 6.4)
- PointLiesOnLine(E, Line(A, N))
- Perpendicular(Line(B, E), Line(E, A))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 57.9 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(MeasureOf(Angle(N, B, E)), 45)",
"Equals(LengthOf(Line(A, N)), 12.8)",
"Equals(LengthOf(Line(B, N)), 6.4)",
"PointLiesOnLine(E, Line(A, N))",
"Perpendicular(Line(B, E), Line(E, A))"
] | [
"CB",
"BN",
"NA",
"AC",
"BE",
"AE",
"NE"
] | {"A": [92.0, 112.0], "B": [200.0, 22.0], "C": [3.0, 22.0], "N": [295.0, 114.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), x)
- Equals(LengthOf(Line(A, C)), y)
- Equals(LengthOf(Line(A, B)), 32)
- Equals(MeasureOf(Angle(B, A, C)), 60)
- Perpendicular(Line(B, C), Line(A, C))
Find y | 16 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), x)",
"Equals(LengthOf(Line(A, C)), y)",
"Equals(LengthOf(Line(A, B)), 32)",
"Equals(MeasureOf(Angle(B, A, C)), 60)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [210.0, 120.0], "B": [2.7001871287934307, 0.01952648279228697], "C": [208.0246516613076, 1.9860664523043923]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, M, E)), z)
- Equals(MeasureOf(Angle(K, I, P)), 4x+6)
- Equals(MeasureOf(Angle(I, L, R)), 2y+8)
- Equals(MeasureOf(Angle(R, L, P)), 142)
- PointLiesOnLine(M, Line(E, P))
- Parallel(Line(J,N), Line(H,K))
- Parallel(Line(B,R), Line(H,K))
Find $y$ in the figure. | 15 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(J, M, E)), z)",
"Equals(MeasureOf(Angle(K, I, P)), 4x+6)",
"Equals(MeasureOf(Angle(I, L, R)), 2y+8)",
"Equals(MeasureOf(Angle(R, L, P)), 142)",
"PointLiesOnLine(M, Line(E, P))",
"Parallel(Line(J,N), Line(H,K))",
"Parallel(Line(B,R), Line(H,K))"
] | [
"BL",
"BR",
"EI",
"EL",
"EM",
"EP",
"HI",
"HK",
"IK",
"IL",
"IP",
"JM",
"JN",
"LP",
"LR",
"MI",
"ML",
"MN",
"MP"
] | {"A": [283.0, 124.0], "B": [5.0, 223.0], "C": [133.0, 26.0], "D": [337.0, 221.0], "E": [354.0, 0.0], "F": [120.0, 125.0], "G": [244.0, 221.0], "H": [2.0, 125.0], "I": [195.0, 125.0], "J": [0.0, 28.0], "K": [361.0, 125.0], "L": [70.0, 223.0], "M": [320.0, 27.0], "N": [361.0, 27.0], "O": [267.0, 221.0], "P": [24.0, 259.0... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 32)
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(G, Line(A, D))
- PointLiesOnLine(F, Line(C, B))
- PointLiesOnLine(H, Line(D, B))
- PointLiesOnCircle(E, Circle(O, radius_5_0))
- PointLiesOnCircle(F, Circle(O, radius_5_0))
- PointLiesOnCircle(G, Circle(O, radius_5... | 32 \pi | [
"Find(CircumferenceOf(Circle($)))"
] | [
"Equals(LengthOf(Line(A, C)), 32)",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(G, Line(A, D))",
"PointLiesOnLine(F, Line(C, B))",
"PointLiesOnLine(H, Line(D, B))",
"PointLiesOnCircle(E, Circle(O, radius_5_0))",
"PointLiesOnCircle(F, Circle(O, radius_5_0))",
"PointLiesOnCircle(G, Circle(O, radi... | [
"AC",
"AD",
"AE",
"AG",
"BF",
"BH",
"CB",
"CE",
"CF",
"DB",
"DG",
"DH"
] | {"A": [234.0, 234.0], "B": [0.0, 0.0], "C": [234.0, 1.0], "D": [1.0, 233.0], "E": [233.0, 120.0], "F": [118.0, 1.0], "G": [116.0, 233.0], "H": [1.0, 120.0], "O": [117.0, 120.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, A, D)), 3x-9)
- Equals(MeasureOf(Angle(B, X, E)), 2.5x+15)
- PointLiesOnLine(X, Line(A, B))
- PointLiesOnLine(A, Line(B, C))
- PointLiesOnLine(X, Line(B, C))
- PointLiesOnLine(A, Line(X, C))
- PointLiesOnLine(A, Line(D, F))
- PointLiesOnLine(X, Line(E, G))
Find $x$. | 48 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, A, D)), 3x-9)",
"Equals(MeasureOf(Angle(B, X, E)), 2.5x+15)",
"PointLiesOnLine(X, Line(A, B))",
"PointLiesOnLine(A, Line(B, C))",
"PointLiesOnLine(X, Line(B, C))",
"PointLiesOnLine(A, Line(X, C))",
"PointLiesOnLine(A, Line(D, F))",
"PointLiesOnLine(X, Line(E, G))"
] | [
"AB",
"AC",
"AD",
"AF",
"AX",
"BC",
"BX",
"DF",
"EG",
"XC",
"XE",
"XG"
] | {"A": [112.0, 90.0], "B": [420.0, 22.0], "C": [0.0, 115.0], "D": [130.0, 2.0], "E": [255.0, 150.0], "F": [100.0, 149.0], "G": [286.0, 1.0], "X": [275.0, 54.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 14)
- Equals(LengthOf(Line(C, D)), 20)
- PointLiesOnLine(B, Line(E, D))
- PointLiesOnCircle(D, Circle(B, radius_1_0))
- PointLiesOnCircle(E, Circle(B, radius_1_0))
-
Find the area of the composite figure. Round to the nearest tenth. | 357.0 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, C)), 14)",
"Equals(LengthOf(Line(C, D)), 20)",
"PointLiesOnLine(B, Line(E, D))",
"PointLiesOnCircle(D, Circle(B, radius_1_0))",
"PointLiesOnCircle(E, Circle(B, radius_1_0))",
""
] | [
"AC",
"AE",
"AH",
"CD",
"EH"
] | {"A": [1.0, 0.0], "B": [206.0, 95.0], "C": [1.0, 189.0], "D": [206.0, 184.0], "E": [207.0, 4.0], "H": [234.0, 4.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 18)
- Equals(LengthOf(Line(B, C)), x)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Perpendicular(Line(B, C), Line(A, C))
Find x. | 9 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(B, C)), x)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.0064374705180654, 156.324703793113], "B": [156.0, 1.0], "C": [154.0189889025894, 155.01257706535142]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 4)
- Equals(LengthOf(Line(B, D)), 9)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(C, D)), z)
- Equals(LengthOf(Line(B, C)), y)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(B, D), Line(C, D))
- Perpendicular(Line(A, C), Line(B, C))
Find z. | 6 | [
"Find(z)"
] | [
"Equals(LengthOf(Line(A, D)), 4)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(C, D)), z)",
"Equals(LengthOf(Line(B, C)), y)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(B, D), Line(C, D))",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CDd"
] | {"A": [1.0, 1.0], "B": [287.0, 140.0], "C": [2.0, 139.0], "D": [57.0, 28.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 21)
- Equals(LengthOf(Line(D, C)), 9)
- Equals(LengthOf(Line(A, E)), 16)
- Equals(LengthOf(Line(B, F)), 7)
- Equals(LengthOf(Line(E, B)), 6)
- Perpendicular(Line(A, D), Line(A, E))
- Perpendicular(Line(A, D), Line(D, C))
- Perpendicular(Line(D, C), Line(F, C))
- Perpen... | 231 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(A, D)), 21)",
"Equals(LengthOf(Line(D, C)), 9)",
"Equals(LengthOf(Line(A, E)), 16)",
"Equals(LengthOf(Line(B, F)), 7)",
"Equals(LengthOf(Line(E, B)), 6)",
"Perpendicular(Line(A, D), Line(A, E))",
"Perpendicular(Line(A, D), Line(D, C))",
"Perpendicular(Line(D, C), Line(F, C))",
... | [
"AD",
"AE",
"BF",
"DC",
"EB",
"FC"
] | {"A": [0.0, 0.0], "B": [70.0, 187.0], "C": [246.0, 106.0], "D": [247.0, 1.0], "E": [2.0, 189.0], "F": [69.0, 106.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Y, X, W)), a)
- Equals(MeasureOf(Angle(W, Z, Y)), a+2)
- Equals(MeasureOf(Angle(A, B, Z)), \frac{1}{2}a+8)
- Equals(MeasureOf(Angle(X, Y, Z)), a-28)
Find $m \angle X$ | 108 | [
"Find(MeasureOf(Angle(X)))"
] | [
"Equals(MeasureOf(Angle(Y, X, W)), a)",
"Equals(MeasureOf(Angle(W, Z, Y)), a+2)",
"Equals(MeasureOf(Angle(A, B, Z)), \\frac{1}{2}a+8)",
"Equals(MeasureOf(Angle(X, Y, Z)), a-28)"
] | [
"AB",
"WA",
"WB",
"WZ",
"XA",
"XW",
"XY",
"YZ",
"ZB"
] | {"A": [28.0, 58.0], "B": [29.0, 100.0], "W": [0.0, 96.0], "X": [70.0, 0.0], "Y": [191.0, 40.0], "Z": [152.0, 115.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), \frac{3}{2}x+11)
- Equals(LengthOf(Line(D, B)), 3y-9)
- Equals(LengthOf(Line(A, D)), x+2)
- Equals(LengthOf(Line(Y, D)), 2x+6)
- PointLiesOnLine(A, Line(C, Y))
- PointLiesOnLine(D, Line(Y, B))
- Equals(LengthOf(Line(D, B)), LengthOf(Line(Y, D)))
- Equals(LengthOf(Line(... | 15 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(C, B)), \\frac{3}{2}x+11)",
"Equals(LengthOf(Line(D, B)), 3y-9)",
"Equals(LengthOf(Line(A, D)), x+2)",
"Equals(LengthOf(Line(Y, D)), 2x+6)",
"PointLiesOnLine(A, Line(C, Y))",
"PointLiesOnLine(D, Line(Y, B))",
"Equals(LengthOf(Line(D, B)), LengthOf(Line(Y, D)))",
"Equals(LengthOf(... | [
"AC",
"AD",
"AY",
"CB",
"CY",
"DB",
"YB",
"YD"
] | {"A": [54.0, 145.0], "B": [111.0, 1.0], "C": [1.0, 75.0], "D": [111.0, 107.0], "Y": [112.0, 219.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(T, S, R)), 125)
- Equals(LengthOf(Line(T, S)), 6.8)
- Equals(MeasureOf(Angle(R, T, S)), 24)
- Equals(LengthOf(Line(T, R)), x)
Find x. Round to the nearest tenth. | 10.8 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(T, S, R)), 125)",
"Equals(LengthOf(Line(T, S)), 6.8)",
"Equals(MeasureOf(Angle(R, T, S)), 24)",
"Equals(LengthOf(Line(T, R)), x)"
] | [
"RS",
"TR",
"TS"
] | {"R": [0.0, 39.0], "S": [160.0, 1.0], "T": [313.0, 135.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(X, A, N)), 78)
- Equals(LengthOf(Line(X, A)), 3)
- Equals(LengthOf(Arc(X, N)), x)
- PointLiesOnCircle(X, Circle(A, radius_1_0))
- PointLiesOnCircle(N, Circle(A, radius_1_0))
Find the value of x. | 4.08 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(X, A, N)), 78)",
"Equals(LengthOf(Line(X, A)), 3)",
"Equals(LengthOf(Arc(X, N)), x)",
"PointLiesOnCircle(X, Circle(A, radius_1_0))",
"PointLiesOnCircle(N, Circle(A, radius_1_0))"
] | [
"AN",
"XA"
] | {"A": [139.0, 139.0], "N": [193.0, 12.0], "X": [29.0, 56.0]} | [
"A"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, G, R)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(R, G, A)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(A, G, F)), MeasureOf(angle 8))
- Equals(MeasureOf(Angle(B, A, S)), MeasureOf(angle 4))
- Equals(MeasureOf(A... | 8 | [
"Equals(MeasureOf(Angle(3)),4y+30)",
"Equals(MeasureOf(Angle(7)),7y+6)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(B, G, R)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(F, G, B)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(R, G, A)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(A, G, F)), MeasureOf(angle 8))",
"Equals(MeasureOf(Angle(B, A, S)), MeasureOf(angle 4))",
"Equals(MeasureOf(Ang... | [
"AB",
"AD",
"AH",
"AS",
"BH",
"DS",
"FG",
"GA",
"GB",
"GH",
"RF",
"RG"
] | {"A": [265.0, 209.0], "B": [72.0, 0.0], "D": [108.0, 231.0], "F": [0.0, 85.0], "G": [133.0, 66.0], "H": [336.0, 286.0], "R": [325.0, 41.0], "S": [428.0, 187.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, K)), 12)
- Equals(LengthOf(Line(D, G)), 9)
- PointLiesOnLine(K, Line(H, D))
- PointLiesOnLine(J, Line(D, F))
- PointLiesOnLine(G, Line(D, C))
- PointLiesOnLine(H, Line(F, C))
- PointLiesOnLine(K, Line(F, G))
- PointLiesOnLine(K, Line(C, J))
In $\triangle CDF$, $K$ is the c... | 18 | [
"Triangle(C,D,F)",
"IsCentroidOf(Point(K),Triangle(C,D,F))",
"Equals(LengthOf(Line(D,K)),16)",
"Find(LengthOf(Line(F,G)))"
] | [
"Equals(LengthOf(Line(F, K)), 12)",
"Equals(LengthOf(Line(D, G)), 9)",
"PointLiesOnLine(K, Line(H, D))",
"PointLiesOnLine(J, Line(D, F))",
"PointLiesOnLine(G, Line(D, C))",
"PointLiesOnLine(H, Line(F, C))",
"PointLiesOnLine(K, Line(F, G))",
"PointLiesOnLine(K, Line(C, J))"
] | [
"CG",
"CJ",
"CK",
"DC",
"DF",
"DG",
"DJ",
"DK",
"FC",
"FG",
"FJ",
"FK",
"HC",
"HD",
"HF",
"HK",
"KG",
"KJ"
] | {"C": [1.0, 0.0], "D": [1.0, 363.0], "F": [251.0, 136.0], "G": [0.0, 175.0], "H": [125.0, 67.0], "J": [126.0, 250.0], "K": [84.0, 163.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(C, D))
- PointLiesOnLine(A, Line(E, F))
- Equals(LengthOf(Line(A, F)), 8)
- Equals(LengthOf(Line(A, E)), 20)
- Equals(LengthOf(Line(B, E)), 15)
- Equals(LengthOf(Line(A, C)), LengthOf(Line(A, D)))
- Perpendicular(Line(A, C), Line(A, F))
Find the area of the shaded figure i... | 420 | [
"Find(AreaOf(Shaded(Shape($))))"
] | [
"PointLiesOnLine(A, Line(C, D))",
"PointLiesOnLine(A, Line(E, F))",
"Equals(LengthOf(Line(A, F)), 8)",
"Equals(LengthOf(Line(A, E)), 20)",
"Equals(LengthOf(Line(B, E)), 15)",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(A, D)))",
"Perpendicular(Line(A, C), Line(A, F))"
] | [
"AC",
"AD",
"AE",
"AF",
"CB",
"CD",
"CF",
"DF",
"EB",
"EF"
] | {"A": [148.0, 110.0], "B": [-0.0, 0.0], "C": [149.0, 2.0], "D": [147.0, 221.0], "E": [2.0, 109.0], "F": [206.0, 111.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(M, D)), 6)
- Equals(LengthOf(Line(C, H)), 14)
- Equals(LengthOf(Line(O, H)), 4)
- PointLiesOnLine(O, Line(M, H))
Find the area of the figure. | 54.9 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(M, D)), 6)",
"Equals(LengthOf(Line(C, H)), 14)",
"Equals(LengthOf(Line(O, H)), 4)",
"PointLiesOnLine(O, Line(M, H))"
] | [
"MD",
"HC",
"CD",
"OM",
"OH",
"MH"
] | {"C": [260.0, 153.0], "D": [111.0, 2.0], "H": [2.0, 151.0], "M": [0.0, 1.0], "O": [1.0, 76.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, J)), 3f-6)
- Equals(MeasureOf(Angle(K, J, M)), 56)
- Equals(MeasureOf(Angle(J, M, L)), 3d-2)
- Equals(LengthOf(Line(L, M)), 2f+8)
Find the value of $f$ in the parallelogram | 14 | [
"Parallelogram($)",
"Find(f)"
] | [
"Equals(LengthOf(Line(K, J)), 3f-6)",
"Equals(MeasureOf(Angle(K, J, M)), 56)",
"Equals(MeasureOf(Angle(J, M, L)), 3d-2)",
"Equals(LengthOf(Line(L, M)), 2f+8)"
] | [
"JM",
"KJ",
"KL",
"LM"
] | {"J": [1.0, 2.0], "K": [246.0, 1.0], "L": [334.0, 207.0], "M": [90.0, 208.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, C, B)), 32)
- Equals(MeasureOf(Angle(G, B, A)), 34)
- Equals(LengthOf(Line(A, G)), 15)
- Equals(LengthOf(Line(A, E)), 12)
- PointLiesOnLine(E, Line(B, A))
- PointLiesOnLine(D, Line(B, C))
- PointLiesOnLine(F, Line(A, C))
- PointLiesOnLine(G, Line(A, D))
- Perpendicular(Li... | 24 | [
"IsIncenterOf(Point(J),Angle(A,B,C))",
"Find(MeasureOf(Angle(J,A,C)))"
] | [
"Equals(MeasureOf(Angle(G, C, B)), 32)",
"Equals(MeasureOf(Angle(G, B, A)), 34)",
"Equals(LengthOf(Line(A, G)), 15)",
"Equals(LengthOf(Line(A, E)), 12)",
"PointLiesOnLine(E, Line(B, A))",
"PointLiesOnLine(D, Line(B, C))",
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(G, Line(A, D))",
"Perpendic... | [
"AC",
"AD",
"AE",
"AG",
"BA",
"BC",
"BD",
"BE",
"BG",
"CD",
"FA",
"FB",
"FC",
"FG",
"GC",
"GD",
"GE"
] | {"A": [352.0, 448.0], "B": [2.0, 188.0], "C": [309.0, 1.0], "D": [151.0, 97.0], "E": [140.0, 291.0], "F": [327.0, 186.0], "G": [209.0, 196.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(M, C, N)), 60)
- Equals(MeasureOf(Angle(L, C, R)), 3x+5)
- Equals(MeasureOf(Angle(M, C, R)), x-1)
- PointLiesOnLine(C, Line(M, L))
- PointLiesOnCircle(M, Circle(C, radius_0_0))
- PointLiesOnCircle(N, Circle(C, radius_0_0))
- PointLiesOnCircle(L, Circle(C, radius_0_0))
- Poin... | 137 | [
"Find(MeasureOf(Angle(R,C,L)))"
] | [
"Equals(MeasureOf(Angle(M, C, N)), 60)",
"Equals(MeasureOf(Angle(L, C, R)), 3x+5)",
"Equals(MeasureOf(Angle(M, C, R)), x-1)",
"PointLiesOnLine(C, Line(M, L))",
"PointLiesOnCircle(M, Circle(C, radius_0_0))",
"PointLiesOnCircle(N, Circle(C, radius_0_0))",
"PointLiesOnCircle(L, Circle(C, radius_0_0))",
"... | [
"CL",
"CM",
"CN",
"CR",
"ML",
"MR"
] | {"C": [85.0, 85.0], "L": [69.0, 167.0], "M": [105.0, 3.0], "N": [167.0, 58.0], "R": [41.0, 14.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, A)), 45)
- Equals(MeasureOf(Angle(B, A, C)), 45)
- Equals(LengthOf(Line(B, A)), 6)
- Perpendicular(Line(C, B), Line(C, A))
Find x | 3 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, B, A)), 45)",
"Equals(MeasureOf(Angle(B, A, C)), 45)",
"Equals(LengthOf(Line(B, A)), 6)",
"Perpendicular(Line(C, B), Line(C, A))"
] | [
"CB",
"CA",
"BA"
] | {"C": [103.16422764227643, 0.8308943089431011], "B": [1.4210854715202004e-14, 102.0], "A": [203.00325203252032, 100.66991869918698]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 8)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(B, D)), 16)
- Equals(LengthOf(Line(B, C)), z)
- Equals(LengthOf(Line(A, B)), y)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(A, D), Line(B, D))
- Perpendicular(Line(B, D), Line(A, B))
Find x. | 32 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 8)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(B, D)), 16)",
"Equals(LengthOf(Line(B, C)), z)",
"Equals(LengthOf(Line(A, B)), y)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(A, D), Line(B, D))",
"Perpendicular(Line(B, D), Line(A, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [394.5113119097765, 1.3258147066150414], "B": [64.49995981510392, 147.49702631769037], "C": [1.3347564614607563, 0.0033741908828019973], "D": [63.00215002388916, 0.15910176779742358]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, I)), 30)
- PointLiesOnLine(D, Line(A, B))
- PointLiesOnLine(H, Line(A, B))
- PointLiesOnLine(F, Line(A, D))
- PointLiesOnLine(F, Line(A, I))
- PointLiesOnLine(D, Line(A, H))
- PointLiesOnLine(F, Line(A, H))
- PointLiesOnLine(H, Line(B, D))
- PointLiesOnLine(D, Line(B, F))
-... | 471.2 | [
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(B, I)), 30)",
"PointLiesOnLine(D, Line(A, B))",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(F, Line(A, D))",
"PointLiesOnLine(F, Line(A, I))",
"PointLiesOnLine(D, Line(A, H))",
"PointLiesOnLine(F, Line(A, H))",
"PointLiesOnLine(H, Line(B, D))",
"PointLiesOnLine(D, Line(B... | [
"AB",
"AD",
"AF",
"AG",
"AH",
"AI",
"BD",
"BF",
"BG",
"BH",
"BI",
"CE",
"CO",
"DF",
"DH",
"DI",
"FG",
"FH",
"FI",
"HO",
"IC",
"IO"
] | {"A": [55.0, 88.0], "B": [124.0, 62.0], "C": [67.0, 164.0], "D": [86.0, 73.0], "E": [83.0, 138.0], "F": [69.0, 79.0], "G": [45.0, 103.0], "H": [99.0, 68.0], "I": [136.0, 39.0], "O": [102.0, 100.0]} | [
"O",
"H"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), 74)
- Equals(MeasureOf(Angle(D, C, B)), x)
- Equals(MeasureOf(Angle(A, D, C)), 105)
- Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))
- Equals(LengthOf(Line(B, C)), LengthOf(Line(D, C)))
If quadrilateral ABCD is a kite, what is $m \angle C$? | 76 | [
"Kite(A,B,C,D)",
"Find(MeasureOf(Angle(C)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), 74)",
"Equals(MeasureOf(Angle(D, C, B)), x)",
"Equals(MeasureOf(Angle(A, D, C)), 105)",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))",
"Equals(LengthOf(Line(B, C)), LengthOf(Line(D, C)))"
] | [
"BA",
"CB",
"CD",
"DA"
] | {"A": [1.0, 109.0], "B": [187.0, 1.0], "C": [343.0, 112.0], "D": [189.0, 216.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, G, E)), 55)
- Equals(MeasureOf(Angle(E, B, H)), y)
- Equals(MeasureOf(Angle(B, G, A)), x)
- PointLiesOnLine(G, Line(A, C))
- PointLiesOnLine(B, Line(G, F))
- PointLiesOnLine(G, Line(B, E))
- PointLiesOnLine(B, Line(D, H))
- PointLiesOnLine(B, Line(E, F))
- PointLiesOnLine... | 125 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(A, G, E)), 55)",
"Equals(MeasureOf(Angle(E, B, H)), y)",
"Equals(MeasureOf(Angle(B, G, A)), x)",
"PointLiesOnLine(G, Line(A, C))",
"PointLiesOnLine(B, Line(G, F))",
"PointLiesOnLine(G, Line(B, E))",
"PointLiesOnLine(B, Line(D, H))",
"PointLiesOnLine(B, Line(E, F))",
"PointLie... | [
"AC",
"AG",
"BD",
"BE",
"BF",
"BH",
"CG",
"DH",
"EF",
"GB",
"GE",
"GF"
] | {"A": [333.0, 154.0], "B": [88.0, 74.0], "C": [0.0, 214.0], "D": [333.0, 28.0], "E": [264.0, 241.0], "F": [11.0, 0.0], "G": [198.0, 178.0], "H": [0.0, 90.0]} | [
""
] |
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... | 127 | [
"Equals(MeasureOf(Angle(1)),53)",
"Find(MeasureOf(Angle(2)))"
] | [
"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(U, D, R)), 179)
- Equals(MeasureOf(Angle(R, D, T)), 71)
- PointLiesOnLine(T, Line(S, U))
- PointLiesOnCircle(R, Circle(D, radius_3_0))
- PointLiesOnCircle(U, Circle(D, radius_3_0))
- PointLiesOnCircle(T, Circle(D, radius_3_0))
Find $m \angle S$. | 54 | [
"Find(MeasureOf(Angle(S)))"
] | [
"Equals(MeasureOf(Angle(U, D, R)), 179)",
"Equals(MeasureOf(Angle(R, D, T)), 71)",
"PointLiesOnLine(T, Line(S, U))",
"PointLiesOnCircle(R, Circle(D, radius_3_0))",
"PointLiesOnCircle(U, Circle(D, radius_3_0))",
"PointLiesOnCircle(T, Circle(D, radius_3_0))"
] | [
"UT",
"US",
"TS",
"RS"
] | {"R": [245.0, 369.0], "S": [373.0, 366.0], "T": [355.0, 319.0], "U": [279.0, 95.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, Y)), 5)
- Equals(LengthOf(Line(A, N)), x)
- Equals(LengthOf(Line(A, B)), z)
- Equals(LengthOf(Line(Y, N)), y)
- Equals(LengthOf(Line(Y, B)), 14)
- PointLiesOnLine(N, Line(Y, B))
- Perpendicular(Line(A, Y), Line(A, B))
- Perpendicular(Line(A, N), Line(B, N))
Find x. | \frac { 15 } { 14 } \sqrt { 19 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, Y)), 5)",
"Equals(LengthOf(Line(A, N)), x)",
"Equals(LengthOf(Line(A, B)), z)",
"Equals(LengthOf(Line(Y, N)), y)",
"Equals(LengthOf(Line(Y, B)), 14)",
"PointLiesOnLine(N, Line(Y, B))",
"Perpendicular(Line(A, Y), Line(A, B))",
"Perpendicular(Line(A, N), Line(B, N))"
] | [
"AB",
"AN",
"AY",
"BN",
"YB",
"YN"
] | {"A": [322.0, 2.0], "B": [320.0, 174.0], "N": [248.0, 135.0], "Y": [0.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, E, P)), 3x-50)
- Equals(MeasureOf(Angle(C, D, G)), 2x-5)
- PointLiesOnLine(D, Line(A, C))
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(E, Line(A, D))
- PointLiesOnLine(D, Line(C, E))
- PointLiesOnLine(D, Line(C, H))
- PointLiesOnLine(E, Line(D, H))
- PointLiesOnLine... | 45 | [
"Parallel(Line(p),Line(q))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, E, P)), 3x-50)",
"Equals(MeasureOf(Angle(C, D, G)), 2x-5)",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(D, Line(C, E))",
"PointLiesOnLine(D, Line(C, H))",
"PointLiesOnLine(E, Line(D, H))",
"PointLie... | [
"AC",
"AD",
"AE",
"CD",
"CE",
"DE",
"DF",
"DG",
"EB",
"EP",
"FG",
"PB"
] | {"A": [0.0, 126.0], "B": [103.0, 203.0], "C": [333.0, 71.0], "D": [213.0, 91.0], "E": [133.0, 104.0], "F": [240.0, 1.0], "G": [180.0, 204.0], "P": [162.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, P)), 10)
- Equals(LengthOf(Line(W, X)), 4)
- Equals(LengthOf(Line(Q, P)), 7)
- Equals(LengthOf(Line(Q, M)), 8)
- Equals(LengthOf(Line(N, M)), 9)
If $MNPQ \sim XYZW,$ find the scale factor of $MNPQ$ to $XYZW$. | 2 | [
"Similar(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W))",
"Find(ScaleFactorOf(Quadrilateral(M,N,P,Q),Quadrilateral(X,Y,Z,W)))"
] | [
"Equals(LengthOf(Line(N, P)), 10)",
"Equals(LengthOf(Line(W, X)), 4)",
"Equals(LengthOf(Line(Q, P)), 7)",
"Equals(LengthOf(Line(Q, M)), 8)",
"Equals(LengthOf(Line(N, M)), 9)"
] | [
"NM",
"PN",
"PQ",
"QM",
"ZW",
"WX",
"XY",
"YZ"
] | {"M": [1.0, 232.0], "N": [188.0, 1.0], "P": [512.0, 102.0], "Q": [300.0, 198.0], "X": [-100.0, 1.0], "W": [-200.0, 5.0], "Y": [-150.0, 150.0], "Z": [-300.0, 75.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(S, M)), 3x+5)
- Equals(LengthOf(Line(S, P)), 6x-7)
- PointLiesOnLine(S, Line(J, B))
- PointLiesOnLine(P, Line(J, T))
- PointLiesOnLine(M, Line(J, C))
- Perpendicular(Line(S, M), Line(J, M))
- Perpendicular(Line(S, P), Line(T, P))
- Equals(MeasureOf(Angle(M, J, S)), MeasureOf(A... | 17 | [
"Find(LengthOf(Line(S,P)))"
] | [
"Equals(LengthOf(Line(S, M)), 3x+5)",
"Equals(LengthOf(Line(S, P)), 6x-7)",
"PointLiesOnLine(S, Line(J, B))",
"PointLiesOnLine(P, Line(J, T))",
"PointLiesOnLine(M, Line(J, C))",
"Perpendicular(Line(S, M), Line(J, M))",
"Perpendicular(Line(S, P), Line(T, P))",
"Equals(MeasureOf(Angle(M, J, S)), Measure... | [
"CP",
"JB",
"JC",
"JM",
"JP",
"JS",
"JT",
"MC",
"SB",
"SM",
"SP",
"TP"
] | {"B": [306.0, 87.0], "C": [196.0, 1.0], "J": [1.0, 214.0], "M": [118.0, 84.0], "P": [178.0, 213.0], "S": [181.0, 141.0], "T": [289.0, 212.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B,C, D)), MeasureOf(angle 10))
- Equals(MeasureOf(Angle(B,C, E)), MeasureOf(angle 9))
- PointLiesOnLine(C, Line(A, B))
- PointLiesOnLine(C, Line(D, E))
$m∠9 = 2x - 4$, $m∠10 = 2x + 4$. Find the measure of $∠9$. | 86 | [
"Equals(MeasureOf(Angle(9)),2x-4)",
"Equals(MeasureOf(Angle(10)),2x+4)",
"Find(MeasureOf(Angle(9)))"
] | [
"Equals(MeasureOf(Angle(B,C, D)), MeasureOf(angle 10))",
"Equals(MeasureOf(Angle(B,C, E)), MeasureOf(angle 9))",
"PointLiesOnLine(C, Line(A, B))",
"PointLiesOnLine(C, Line(D, E))"
] | [
"AB",
"AC",
"BC",
"CD",
"CE",
"DE"
] | {"A": [183.0, 77.0], "B": [0.0, 77.0], "C": [95.0, 77.0], "D": [123.0, 1.0], "E": [70.0, 145.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Arc(J, B, L)), 58)
- Equals(MeasureOf(Arc(M, B, C)), 164)
- PointLiesOnLine(M, Line(K, A))
- PointLiesOnLine(L, Line(K, A))
- PointLiesOnLine(J, Line(K, C))
- PointLiesOnLine(L, Line(K, M))
- PointLiesOnLine(L, Line(K, D))
- PointLiesOnLine(M, Line(A, L))
- PointLiesOnCircle(M, Ci... | 53 | [
"Find(MeasureOf(Angle(K)))"
] | [
"Equals(MeasureOf(Arc(J, B, L)), 58)",
"Equals(MeasureOf(Arc(M, B, C)), 164)",
"PointLiesOnLine(M, Line(K, A))",
"PointLiesOnLine(L, Line(K, A))",
"PointLiesOnLine(J, Line(K, C))",
"PointLiesOnLine(L, Line(K, M))",
"PointLiesOnLine(L, Line(K, D))",
"PointLiesOnLine(M, Line(A, L))",
"PointLiesOnCircl... | [
"AD",
"AL",
"AM",
"CJ",
"KA",
"KC",
"KD",
"KJ",
"KL",
"KM",
"LD",
"MD",
"ML"
] | {"A": [0.0, 203.0], "B": [186.0, 122.0], "C": [286.0, 237.0], "D": [14.0, 185.0], "J": [286.0, 121.0], "K": [285.0, 1.0], "L": [239.0, 34.0], "M": [86.0, 143.0]} | [
"B"
] |
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(... | 6 | [
"IsMidpointOf(Point(J),Line(K,H))",
"IsMidpointOf(Point(P),Line(H,M))",
"IsMidpointOf(Point(L),Line(M,K))",
"Find(y)"
] | [
"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(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(... | 1 | [
"IsMidpointOf(Point(J),Line(K,H))",
"IsMidpointOf(Point(P),Line(H,M))",
"IsMidpointOf(Point(L),Line(M,K))",
"Find(z)"
] | [
"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(T, A)), 14x-34)
- Equals(LengthOf(Line(R, A)), 12x-8)
- PointLiesOnLine(A, Line(Q, S))
- PointLiesOnLine(A, Line(R, T))
If QRST is a parallelogram, what is the value of x? | 13 | [
"Parallelogram(Q,R,S,T)",
"Find(x)"
] | [
"Equals(LengthOf(Line(T, A)), 14x-34)",
"Equals(LengthOf(Line(R, A)), 12x-8)",
"PointLiesOnLine(A, Line(Q, S))",
"PointLiesOnLine(A, Line(R, T))"
] | [
"QA",
"QR",
"QS",
"QT",
"RA",
"RS",
"RT",
"SA",
"TA",
"TS"
] | {"A": [242.0, 114.0], "Q": [121.0, 2.0], "R": [482.0, 1.0], "S": [363.0, 226.0], "T": [0.0, 226.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(C, B))
- PointLiesOnLine(D, Line(B, A))
- PointLiesOnCircle(C, Circle(F, radius_5_0))
- PointLiesOnCircle(B, Circle(F, radius_5_0))
- PointLiesOnCircle(A, Circle(F, radius_5_0))
- Perpendicular(Line(C, E), Line(E, F))
- Perpendicular(Line(D, F), Line(D, A))
In $\odot F$, $... | 8 | [
"Circle(F)",
"Equals(LengthOf(Line(A,B)),Line(B,C))",
"Equals(LengthOf(Line(D,F)),3x-7)",
"Equals(LengthOf(Line(F,E)),x+9)",
"Find(x)"
] | [
"PointLiesOnLine(E, Line(C, B))",
"PointLiesOnLine(D, Line(B, A))",
"PointLiesOnCircle(C, Circle(F, radius_5_0))",
"PointLiesOnCircle(B, Circle(F, radius_5_0))",
"PointLiesOnCircle(A, Circle(F, radius_5_0))",
"Perpendicular(Line(C, E), Line(E, F))",
"Perpendicular(Line(D, F), Line(D, A))"
] | [
"BA",
"BD",
"CB",
"CE",
"DA",
"EB",
"EF",
"FD"
] | {"A": [80.0, 277.0], "B": [58.0, 32.0], "C": [285.0, 115.0], "D": [68.0, 153.0], "E": [172.0, 73.0], "F": [143.0, 146.0]} | [
"F"
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(A, D))
- Perpendicular(Line(B, D), Line(D, T))
Find $x$. A = 153 in$^2$. | 17 | [
"Equals(AreaOf(Shape(A)),153)",
"Find(x)"
] | [
"PointLiesOnLine(T, Line(A, D))",
"Perpendicular(Line(B, D), Line(D, T))"
] | [
"AC",
"AT",
"CB",
"TB",
"BD",
"DT",
"AD"
] | {"A": [287.0, 129.0], "B": [0.0, 0.0], "C": [221.0, 1.0], "T": [65.0, 129.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, B, C)), 10)
- Equals(LengthOf(Line(B, C)), 3)
- PointLiesOnCircle(A, Circle(B, radius_1_0))
- PointLiesOnCircle(C, Circle(B, radius_1_0))
What is the area of the sector? | \frac { \pi } { 4 } | [
"Find(AreaOf(Sector($)))"
] | [
"Equals(MeasureOf(Angle(A, B, C)), 10)",
"Equals(LengthOf(Line(B, C)), 3)",
"PointLiesOnCircle(A, Circle(B, radius_1_0))",
"PointLiesOnCircle(C, Circle(B, radius_1_0))"
] | [
"AB",
"AC",
"BC"
] | {"A": [2.0, 90.0], "B": [109.0, 109.0], "C": [8.0, 107.0]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, M, L)), 2x-8)
- Equals(MeasureOf(Angle(M, J, K)), 3x-6)
- Equals(MeasureOf(Angle(J, K, L)), x+10)
- Equals(MeasureOf(Angle(K, L, M)), x)
Find $m\angle J$ | 150 | [
"Find(MeasureOf(Angle(J)))"
] | [
"Equals(MeasureOf(Angle(J, M, L)), 2x-8)",
"Equals(MeasureOf(Angle(M, J, K)), 3x-6)",
"Equals(MeasureOf(Angle(J, K, L)), x+10)",
"Equals(MeasureOf(Angle(K, L, M)), x)"
] | [
"KJ",
"LK",
"LM",
"MJ"
] | {"J": [121.0, 43.0], "K": [1.0, 206.0], "L": [412.0, 206.0], "M": [288.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 3)
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(A, C, B)), 45)
- Equals(LengthOf(Line(B, C)), y)
- Perpendicular(Line(A, C), Line(A, B))
Find x | 3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 3)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(A, C, B)), 45)",
"Equals(LengthOf(Line(B, C)), y)",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"BC"
] | {"A": [144.5051903114187, 1.4809688581314902], "B": [287.28716950041195, 138.0039947070132], "C": [2.6703159291583916, 139.99645281478078]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 8)
- Equals(LengthOf(Line(R, Q)), 4)
- Equals(LengthOf(Line(K, J)), 6)
- Equals(LengthOf(Line(L, K)), 12)
- Equals(MeasureOf(Angle(R, Q, S)), 80)
- Equals(MeasureOf(Angle(Q, S, R)), x)
- Equals(MeasureOf(Angle(K, L, J)), 30)
- Equals(MeasureOf(Angle(J, K, L)), y)
- Equ... | 70 | [
"Similar(Polygon($1),Polygon($2))",
"Find(y)"
] | [
"Equals(LengthOf(Line(R, S)), 8)",
"Equals(LengthOf(Line(R, Q)), 4)",
"Equals(LengthOf(Line(K, J)), 6)",
"Equals(LengthOf(Line(L, K)), 12)",
"Equals(MeasureOf(Angle(R, Q, S)), 80)",
"Equals(MeasureOf(Angle(Q, S, R)), x)",
"Equals(MeasureOf(Angle(K, L, J)), 30)",
"Equals(MeasureOf(Angle(J, K, L)), y)",... | [
"JL",
"KJ",
"KL",
"QS",
"RQ",
"RS"
] | {"J": [1.0, 178.0], "K": [31.0, 0.0], "L": [344.0, 180.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), LengthOf(c))
- Equals(LengthOf(Line(C, B)), LengthOf(a))
- Equals(LengthOf(Line(A, C)), LengthOf(b))
- Perpendicular(Line(C, B), Line(A, C))
$a=8, b=15,$ and $c=17$ find $tanB$ | 1.88 | [
"Equals(a,8)",
"Equals(b,15)",
"Equals(c,17)",
"Find(TanOf(Angle(B)))"
] | [
"Equals(LengthOf(Line(A, B)), LengthOf(c))",
"Equals(LengthOf(Line(C, B)), LengthOf(a))",
"Equals(LengthOf(Line(A, C)), LengthOf(b))",
"Perpendicular(Line(C, B), Line(A, C))"
] | [
"AC",
"AB",
"CB"
] | {"A": [162.0, 90.0], "C": [0.9878021062201725, 87.99977271005379], "B": [0.0, 4.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, M, E)), z)
- Equals(MeasureOf(Angle(K, I, P)), 4x+6)
- Equals(MeasureOf(Angle(I, L, R)), 2y+8)
- Equals(MeasureOf(Angle(R, L, P)), 142)
- PointLiesOnLine(M, Line(E, P))
- Parallel(Line(J,N), Line(H,K))
- Parallel(Line(B,R), Line(H,K))
Find $z$ in the figure. | 142 | [
"Find(z)"
] | [
"Equals(MeasureOf(Angle(J, M, E)), z)",
"Equals(MeasureOf(Angle(K, I, P)), 4x+6)",
"Equals(MeasureOf(Angle(I, L, R)), 2y+8)",
"Equals(MeasureOf(Angle(R, L, P)), 142)",
"PointLiesOnLine(M, Line(E, P))",
"Parallel(Line(J,N), Line(H,K))",
"Parallel(Line(B,R), Line(H,K))"
] | [
"BL",
"BR",
"EI",
"EL",
"EM",
"EP",
"HI",
"HK",
"IK",
"IL",
"IP",
"JM",
"JN",
"LP",
"LR",
"MI",
"ML",
"MN",
"MP"
] | {"A": [283.0, 124.0], "B": [5.0, 223.0], "C": [133.0, 26.0], "D": [337.0, 221.0], "E": [354.0, 0.0], "F": [120.0, 125.0], "G": [244.0, 221.0], "H": [2.0, 125.0], "I": [195.0, 125.0], "J": [0.0, 28.0], "K": [361.0, 125.0], "L": [70.0, 223.0], "M": [320.0, 27.0], "N": [361.0, 27.0], "O": [267.0, 221.0], "P": [24.0, 259.0... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, D, G)), 36)
- Equals(MeasureOf(Angle(D, G, A)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, G, C)), 104)
- Equals(MeasureOf(Angle(E, F, C)), 40)
- Equals(MeasureOf(Angle(C, G, B)), MeasureOf(angle 3))
- Equals(Me... | 76 | [
"Perpendicular(Line(A,B),Line(B,C))",
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, D, G)), 36)",
"Equals(MeasureOf(Angle(D, G, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, G, C)), 104)",
"Equals(MeasureOf(Angle(E, F, C)), 40)",
"Equals(MeasureOf(Angle(C, G, B)), MeasureOf(angle 3))",
"Equals(M... | [
"AB",
"AD",
"AG",
"BC",
"BE",
"BF",
"BG",
"CF",
"DC",
"DF",
"DG",
"FE",
"GC",
"GF"
] | {"A": [113.0, 1.0], "B": [153.0, 162.0], "C": [469.0, 84.0], "D": [1.0, 84.0], "E": [346.0, 1.0], "F": [247.0, 84.0], "G": [134.0, 83.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, B, A)), 60)
- Equals(LengthOf(Line(C, B)), 14)
- Perpendicular(Line(A, B), Line(A, C))
Find AC | 7 \sqrt { 3 } | [
"Find(LengthOf(Line(A,C)))"
] | [
"Equals(MeasureOf(Angle(C, B, A)), 60)",
"Equals(LengthOf(Line(C, B)), 14)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"CB"
] | {"A": [1.0, 138.0], "B": [1.0, 1.0], "C": [242.0, 137.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, G, K)), 194)
- PointLiesOnCircle(K, Circle(G, radius_8_0))
- PointLiesOnCircle(J, Circle(G, radius_8_0))
- Perpendicular(Line(L,K), Line(J,K))
Find $m \angle K$. | 97 | [
"Find(MeasureOf(Angle(K)))"
] | [
"Equals(MeasureOf(Angle(J, G, K)), 194)",
"PointLiesOnCircle(K, Circle(G, radius_8_0))",
"PointLiesOnCircle(J, Circle(G, radius_8_0))",
"Perpendicular(Line(L,K), Line(J,K))"
] | [
"JK",
"KL"
] | {"G": [238.0, 240.0], "J": [108.0, 294.0], "K": [376.0, 220.0], "L": [342.0, 71.0]} | [
"G"
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(J, L))
- PointLiesOnLine(R, Line(J, K))
- PointLiesOnLine(P, Line(J, S))
- PointLiesOnLine(S, Line(L, K))
- PointLiesOnLine(P, Line(L, R))
- PointLiesOnLine(P, Line(K, T))
- Equals(LengthOf(Line(K, R)), LengthOf(Line(R, J)))
- Equals(LengthOf(Line(L, T)), LengthOf(Line(T, J... | 4 | [
"Triangle(J,K,L)",
"Equals(LengthOf(Line(P,T)),2)",
"Find(LengthOf(Line(K,P)))"
] | [
"PointLiesOnLine(T, Line(J, L))",
"PointLiesOnLine(R, Line(J, K))",
"PointLiesOnLine(P, Line(J, S))",
"PointLiesOnLine(S, Line(L, K))",
"PointLiesOnLine(P, Line(L, R))",
"PointLiesOnLine(P, Line(K, T))",
"Equals(LengthOf(Line(K, R)), LengthOf(Line(R, J)))",
"Equals(LengthOf(Line(L, T)), LengthOf(Line(... | [
"JS",
"JC",
"JK",
"JL",
"JR",
"JT",
"KS",
"KR",
"KT",
"LS",
"LC",
"LK",
"LR",
"LT",
"PS",
"PJ",
"PK",
"PL",
"PR",
"PT",
"TC"
] | {"S": [365.0, 33.0], "C": [151.0, 284.0], "J": [1.0, 374.0], "K": [202.0, 4.0], "L": [541.0, 62.0], "P": [248.0, 143.0], "R": [105.0, 182.0], "T": [271.0, 218.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, Y, X)), 2x)
- Equals(MeasureOf(Angle(Y, X, W)), x)
- Equals(MeasureOf(Angle(X, W, Z)), 3x)
- Equals(MeasureOf(Angle(W, Z, Y)), 4x)
Find $m\angle Z$ | 144 | [
"Find(MeasureOf(Angle(Z)))"
] | [
"Equals(MeasureOf(Angle(Z, Y, X)), 2x)",
"Equals(MeasureOf(Angle(Y, X, W)), x)",
"Equals(MeasureOf(Angle(X, W, Z)), 3x)",
"Equals(MeasureOf(Angle(W, Z, Y)), 4x)"
] | [
"ZY",
"WZ",
"WX",
"XY"
] | {"Z": [247.0, 214.0], "W": [82.0, 214.0], "X": [0.0, 0.0], "Y": [330.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 23)
- Equals(MeasureOf(Angle(B, D, E)), 45)
- Equals(LengthOf(Line(D, E)), 5)
- PointLiesOnLine(E, Line(A, D))
- Perpendicular(Line(B, E), Line(E, A))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 115 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(C, B)), 23)",
"Equals(MeasureOf(Angle(B, D, E)), 45)",
"Equals(LengthOf(Line(D, E)), 5)",
"PointLiesOnLine(E, Line(A, D))",
"Perpendicular(Line(B, E), Line(E, A))"
] | [
"AC",
"AD",
"AE",
"BE",
"CB",
"DB",
"DE"
] | {"A": [81.0, 80.0], "B": [258.0, 2.0], "C": [0.0, 0.0], "D": [337.0, 81.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, E)), 20)
- Equals(LengthOf(Line(D, E)), 30)
- Equals(LengthOf(Line(C, E)), 20)
- Equals(LengthOf(Line(A, E)), 30)
- PointLiesOnLine(E, Line(A, D))
- PointLiesOnLine(E, Line(B, C))
- Perpendicular(Line(B, E), Line(A, E))
Find the area of the figure. Round to the nearest ten... | 1200 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(B, E)), 20)",
"Equals(LengthOf(Line(D, E)), 30)",
"Equals(LengthOf(Line(C, E)), 20)",
"Equals(LengthOf(Line(A, E)), 30)",
"PointLiesOnLine(E, Line(A, D))",
"PointLiesOnLine(E, Line(B, C))",
"Perpendicular(Line(B, E), Line(A, E))"
] | [
"AB",
"AC",
"AD",
"AE",
"BC",
"BD",
"BE",
"CD",
"CE",
"DE"
] | {"A": [0.0, 200.0], "B": [78.0, 2.0], "C": [213.0, 200.0], "D": [291.0, 1.0], "E": [147.0, 101.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(J, M, L)), 2x-8)
- Equals(MeasureOf(Angle(M, J, K)), 3x-6)
- Equals(MeasureOf(Angle(J, K, L)), x+10)
- Equals(MeasureOf(Angle(K, L, M)), x)
Find $m\angle K$ | 62 | [
"Find(MeasureOf(Angle(K)))"
] | [
"Equals(MeasureOf(Angle(J, M, L)), 2x-8)",
"Equals(MeasureOf(Angle(M, J, K)), 3x-6)",
"Equals(MeasureOf(Angle(J, K, L)), x+10)",
"Equals(MeasureOf(Angle(K, L, M)), x)"
] | [
"KJ",
"LK",
"LM",
"MJ"
] | {"J": [121.0, 43.0], "K": [1.0, 206.0], "L": [412.0, 206.0], "M": [288.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, D, C)), 24)
- PointLiesOnCircle(B, Circle(D, radius_3_0))
- PointLiesOnCircle(A, Circle(D, radius_3_0))
- PointLiesOnCircle(C, Circle(D, radius_3_0))
Find $m \widehat {AC}$. | 48 | [
"Find(MeasureOf(Arc(A,C)))"
] | [
"Equals(MeasureOf(Angle(A, D, C)), 24)",
"PointLiesOnCircle(B, Circle(D, radius_3_0))",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(C, Circle(D, radius_3_0))"
] | [
"BA",
"BC"
] | {"A": [14.0, 93.0], "B": [262.0, 276.0], "C": [111.0, 7.0], "D": [157.0, 159.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, J)), 2y+1)
- Equals(LengthOf(Line(A, G)), \frac{1}{5}x+3)
- Equals(LengthOf(Line(J, E)), 5y-8)
- Equals(LengthOf(Line(E, G)), 4x-35)
- PointLiesOnLine(G, Line(A, E))
- PointLiesOnLine(J, Line(C, E))
- Parallel(Line(A, C), Line(G, J))
- Equals(LengthOf(Line(C, J)), LengthOf(... | 10 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, J)), 2y+1)",
"Equals(LengthOf(Line(A, G)), \\frac{1}{5}x+3)",
"Equals(LengthOf(Line(J, E)), 5y-8)",
"Equals(LengthOf(Line(E, G)), 4x-35)",
"PointLiesOnLine(G, Line(A, E))",
"PointLiesOnLine(J, Line(C, E))",
"Parallel(Line(A, C), Line(G, J))",
"Equals(LengthOf(Line(C, J)), Leng... | [
"AC",
"AG",
"GE",
"AE",
"CJ",
"JG",
"JE",
"CE"
] | {"A": [1.0, 12.0], "C": [365.0, 11.0], "E": [184.0, 327.0], "G": [90.0, 167.0], "J": [277.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, D, F)), 3x+2)
- Equals(MeasureOf(Angle(A, F, G)), 2x)
- Equals(MeasureOf(Angle(B, I, D)), x+5)
- Equals(MeasureOf(Angle(C, G, B)), 2x+1)
- PointLiesOnLine(F, Line(A, D))
- PointLiesOnLine(G, Line(F, C))
- PointLiesOnLine(I, Line(G, B))
- PointLiesOnLine(D, Line(I, H))
Fi... | 44 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(H, D, F)), 3x+2)",
"Equals(MeasureOf(Angle(A, F, G)), 2x)",
"Equals(MeasureOf(Angle(B, I, D)), x+5)",
"Equals(MeasureOf(Angle(C, G, B)), 2x+1)",
"PointLiesOnLine(F, Line(A, D))",
"PointLiesOnLine(G, Line(F, C))",
"PointLiesOnLine(I, Line(G, B))",
"PointLiesOnLine(D, Line(I, H))... | [
"AD",
"AF",
"BG",
"BI",
"DF",
"DH",
"DI",
"FC",
"FG",
"GC",
"GI",
"IH"
] | {"A": [385.0, 91.0], "B": [70.0, 238.0], "C": [376.0, 320.0], "D": [23.0, 48.0], "F": [318.0, 81.0], "G": [366.0, 275.0], "H": [3.0, 4.0], "I": [116.0, 237.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), z)
- Equals(LengthOf(Line(A, D)), 8)
- Equals(LengthOf(Line(A, B)), y)
- Equals(MeasureOf(Angle(A, B, C)), 45)
- Equals(MeasureOf(Angle(A, D, B)), 60)
- Equals(LengthOf(Line(B, D)), x)
- Perpendicular(Line(A, C), Line(B, C))
- Perpendicular(Line(A, B), Line(B, D))
Fin... | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), z)",
"Equals(LengthOf(Line(A, D)), 8)",
"Equals(LengthOf(Line(A, B)), y)",
"Equals(MeasureOf(Angle(A, B, C)), 45)",
"Equals(MeasureOf(Angle(A, D, B)), 60)",
"Equals(LengthOf(Line(B, D)), x)",
"Perpendicular(Line(A, C), Line(B, C))",
"Perpendicular(Line(A, B), Line(B, D))"... | [
"AB",
"AC",
"AD",
"BC",
"BD"
] | {"A": [128.67133250256126, 1.5536783226083486], "B": [128.83179792830194, 219.33187314906218], "C": [236.50898890208444, 110.49547483516933], "D": [0.19786910197868224, 220.33333333333331]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, E)), 5)
- Equals(LengthOf(Line(A, C)), 13)
- Equals(LengthOf(Line(A, O)), 12)
- PointLiesOnLine(E, Line(O, A))
- Perpendicular(Line(B, E), Line(A, E))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 60 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(B, E)), 5)",
"Equals(LengthOf(Line(A, C)), 13)",
"Equals(LengthOf(Line(A, O)), 12)",
"PointLiesOnLine(E, Line(O, A))",
"Perpendicular(Line(B, E), Line(A, E))"
] | [
"AC",
"AO",
"CB",
"OB",
"BE",
"OE",
"AE"
] | {"A": [177.0, 126.0], "B": [60.0, 2.0], "C": [237.0, 1.0], "O": [0.0, 126.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(S, T, P)), 150)
- PointLiesOnLine(T, Line(R, P))
- Perpendicular(Line(R, S), Line(T, S))
$ \triangle RST$ is a right triangle. Find $m∠R$. | 60 | [
"Right(Triangle(R,S,T))",
"Find(MeasureOf(Angle(R)))"
] | [
"Equals(MeasureOf(Angle(S, T, P)), 150)",
"PointLiesOnLine(T, Line(R, P))",
"Perpendicular(Line(R, S), Line(T, S))"
] | [
"RS",
"ST",
"RT",
"TP",
"RP"
] | {"S": [2.0, 198.0], "P": [438.0, 254.0], "R": [1.0, 1.0], "T": [346.0, 201.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Q, T)), 2x)
- Equals(LengthOf(Line(T, R)), 8)
- Equals(LengthOf(Line(P, T)), 3y-1)
- Equals(LengthOf(Line(P, G)), z+4)
- Equals(LengthOf(Line(G, R)), 7)
- PointLiesOnLine(F, Line(Q, R))
- PointLiesOnLine(G, Line(P, R))
- PointLiesOnLine(G, Line(P, D))
- PointLiesOnLine(H, Line... | 4 | [
"IsPerpendicularBisectorOf(Line(l),Triangle(P,Q,R))",
"IsPerpendicularBisectorOf(Line(m),Triangle(P,Q,R))",
"IsPerpendicularBisectorOf(Line(n),Triangle(P,Q,R))",
"IntersectAt(Line(l),Line(m),Line(n),Point(T))",
"Equals(LengthOf(Line(T,Q)),2x)",
"Equals(LengthOf(Line(P,T)),3y-1)",
"Equals(LengthOf(Line(T... | [
"Equals(LengthOf(Line(Q, T)), 2x)",
"Equals(LengthOf(Line(T, R)), 8)",
"Equals(LengthOf(Line(P, T)), 3y-1)",
"Equals(LengthOf(Line(P, G)), z+4)",
"Equals(LengthOf(Line(G, R)), 7)",
"PointLiesOnLine(F, Line(Q, R))",
"PointLiesOnLine(G, Line(P, R))",
"PointLiesOnLine(G, Line(P, D))",
"PointLiesOnLine(... | [
"QP",
"QR",
"PR",
"QT",
"TR",
"TP",
"PG",
"PD",
"GD",
"GR",
"DR",
"PH",
"HQ",
"QF",
"FR",
"EZ",
"HZ"
] | {"A": [66.0, 146.0], "C": [199.0, 125.0], "D": [237.0, 195.0], "E": [199.0, 36.0], "F": [387.0, 96.0], "G": [199.0, 194.0], "H": [193.0, 96.0], "I": [419.0, 91.0], "M": [361.0, 10.0], "P": [2.0, 195.0], "Q": [373.0, 2.0], "R": [402.0, 195.0], "T": [167.0, 61.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Z, X)), 14)
- Equals(LengthOf(Line(X, Y)), 7)
- Equals(LengthOf(Line(Z, Y)), x)
- Perpendicular(Line(X, Y), Line(Z, Y))
Find x | 7 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(Z, X)), 14)",
"Equals(LengthOf(Line(X, Y)), 7)",
"Equals(LengthOf(Line(Z, Y)), x)",
"Perpendicular(Line(X, Y), Line(Z, Y))"
] | [
"XY",
"ZX",
"ZY"
] | {"X": [1.0, 1.0], "Y": [0.0, 112.0], "Z": [201.0, 113.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, S)), 4)
- Equals(LengthOf(Line(L, B)), 6)
- Equals(LengthOf(Line(N, B)), 18)
- Equals(LengthOf(Line(A, N)), 21)
- Equals(LengthOf(Line(A, N)), LengthOf(n))
Find the area of the figure. Round to the nearest tenth if necessary. | 99 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(E, S)), 4)",
"Equals(LengthOf(Line(L, B)), 6)",
"Equals(LengthOf(Line(N, B)), 18)",
"Equals(LengthOf(Line(A, N)), 21)",
"Equals(LengthOf(Line(A, N)), LengthOf(n))"
] | [
"AB",
"AN",
"BS",
"LC",
"NS"
] | {"A": [0.0, 157.0], "B": [121.0, 1.0], "C": [130.0, 149.0], "L": [110.0, 144.0], "N": [418.0, 194.0], "S": [348.0, 53.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Q, S, R)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(R, S, M)), MeasureOf(angle 1))
- PointLiesOnLine(S, Line(N, Q))
- PointLiesOnLine(R, Line(Q, M))
- Equals(LengthOf(Line(S, Q)), LengthOf(Line(S, N)))
Find $x$ if $\overline{MS}$ is an altitude of $\triangle MNQ$, $m\an... | 7 | [
"Equals(Line(M,S),AltitudeOf(Triangle(M,N,Q)))",
"Equals(MeasureOf(Angle(1)),3x+11)",
"Equals(MeasureOf(Angle(2)),7x+9)",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(Q, S, R)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(R, S, M)), MeasureOf(angle 1))",
"PointLiesOnLine(S, Line(N, Q))",
"PointLiesOnLine(R, Line(Q, M))",
"Equals(LengthOf(Line(S, Q)), LengthOf(Line(S, N)))"
] | [
"MR",
"NM",
"NQ",
"QM",
"QR",
"SM",
"SN",
"SQ",
"SR"
] | {"M": [169.0, 3.0], "N": [257.0, 139.0], "Q": [0.0, 20.0], "R": [85.0, 11.0], "S": [130.0, 80.0]} | [
""
] |
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 $z$ in the figure. | 42 | [
"Find(z)"
] | [
"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:
- Equals(LengthOf(Line(Q, P)), 2x)
- Equals(LengthOf(Line(R, Q)), 3y+8)
- Equals(LengthOf(Line(R, S)), 2y)
- Equals(LengthOf(Line(P, S)), x)
- PointLiesOnLine(S, Line(R, P))
- Perpendicular(Line(Q, S), Line(R, S))
$\triangle PQS \cong \triangle RQS$. Find $y$. | 8 | [
"Congruent(Triangle(P,Q,S),Triangle(R,Q,S))",
"Find(y)"
] | [
"Equals(LengthOf(Line(Q, P)), 2x)",
"Equals(LengthOf(Line(R, Q)), 3y+8)",
"Equals(LengthOf(Line(R, S)), 2y)",
"Equals(LengthOf(Line(P, S)), x)",
"PointLiesOnLine(S, Line(R, P))",
"Perpendicular(Line(Q, S), Line(R, S))"
] | [
"PS",
"QP",
"QS",
"RP",
"RQ",
"RS"
] | {"P": [1.0, 322.0], "Q": [338.0, 1.0], "R": [674.0, 322.0], "S": [336.0, 322.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Y, X, E)), 31)
- Equals(MeasureOf(Angle(B, Y, G)), 27)
- Equals(LengthOf(Line(A, B)), 20)
- Equals(LengthOf(Line(B, J)), 12)
- PointLiesOnLine(A, Line(L, Y))
- PointLiesOnLine(K, Line(Y, X))
- PointLiesOnLine(J, Line(Y, B))
- PointLiesOnLine(E, Line(A, X))
- PointLiesOnLine(... | 32 | [
"IsIncenterOf(Point(P),Angle(X,Y,Z))",
"Find(MeasureOf(Angle(L,Z,P)))"
] | [
"Equals(MeasureOf(Angle(Y, X, E)), 31)",
"Equals(MeasureOf(Angle(B, Y, G)), 27)",
"Equals(LengthOf(Line(A, B)), 20)",
"Equals(LengthOf(Line(B, J)), 12)",
"PointLiesOnLine(A, Line(L, Y))",
"PointLiesOnLine(K, Line(Y, X))",
"PointLiesOnLine(J, Line(Y, B))",
"PointLiesOnLine(E, Line(A, X))",
"PointLies... | [
"AB",
"AC",
"AD",
"AE",
"AF",
"AG",
"AJ",
"AK",
"AP",
"AX",
"BC",
"BF",
"BG",
"BJ",
"BK",
"BP",
"CF",
"CP",
"DE",
"GC",
"GD",
"GE",
"GF",
"GJ",
"GK",
"GP",
"JD",
"JE",
"KC",
"KF",
"KP",
"LA",
"LB",
"LG",
"LX",
"LY",
"PF",
"XB",
"XD",
"XE"... | {"A": [116.0, 183.0], "B": [14.0, 367.0], "C": [87.0, 242.0], "D": [146.0, 230.0], "E": [86.0, 130.0], "F": [158.0, 105.0], "G": [122.0, 192.0], "J": [174.0, 281.0], "K": [169.0, 82.0], "L": [7.0, 186.0], "P": [140.0, 137.0], "X": [0.0, 2.0], "Y": [367.0, 176.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, B)), 5)
- Equals(LengthOf(Line(A, B)), x-2)
- Equals(LengthOf(Line(A, D)), x)
- Equals(LengthOf(Line(D, G)), 75)
- PointLiesOnLine(B, Line(E, A))
- PointLiesOnLine(D, Line(A, G))
The pair of polygons is similar. Find AB | 4 | [
"Similar(Polygon($1),Polygon($2))",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(E, B)), 5)",
"Equals(LengthOf(Line(A, B)), x-2)",
"Equals(LengthOf(Line(A, D)), x)",
"Equals(LengthOf(Line(D, G)), 75)",
"PointLiesOnLine(B, Line(E, A))",
"PointLiesOnLine(D, Line(A, G))"
] | [
"AB",
"AD",
"AG",
"BC",
"DC",
"DG",
"EA",
"EB",
"EF",
"FG"
] | {"A": [2.0, 156.0], "B": [1.0, 85.0], "C": [99.0, 88.0], "D": [100.0, 155.0], "E": [0.0, 0.0], "F": [229.0, 1.0], "G": [228.0, 154.0]} | [
""
] |
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 $\angle T$ | 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, B)), 6)
- Equals(LengthOf(Line(Y, A)), x)
- Equals(LengthOf(Line(B, C)), y)
- Equals(MeasureOf(Angle(B, C, A)), 45)
- PointLiesOnLine(Y, Line(B, C))
- Perpendicular(Line(A, B), Line(A, C))
- Perpendicular(Line(Y, A), Line(Y, C))
Find y. | 6 \sqrt { 2 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, B)), 6)",
"Equals(LengthOf(Line(Y, A)), x)",
"Equals(LengthOf(Line(B, C)), y)",
"Equals(MeasureOf(Angle(B, C, A)), 45)",
"PointLiesOnLine(Y, Line(B, C))",
"Perpendicular(Line(A, B), Line(A, C))",
"Perpendicular(Line(Y, A), Line(Y, C))"
] | [
"AB",
"AC",
"BC",
"YA",
"YB",
"YC"
] | {"A": [139.0, 1.0], "B": [0.0, 149.0], "C": [276.0, 147.0], "Y": [140.0, 148.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 3\sqrt{2})
- Equals(LengthOf(Line(C, D)), z)
- Equals(LengthOf(Line(B, D)), \sqrt{2})
- Equals(LengthOf(Line(B, C)), y)
- Equals(LengthOf(Line(A, B)), x)
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(C, D), Line(B, D))
- Perpendicular(Line(B, C), Line(A, B))
F... | \frac { 2 } { 3 } \sqrt { 5 } | [
"Find(y)"
] | [
"Equals(LengthOf(Line(A, D)), 3\\sqrt{2})",
"Equals(LengthOf(Line(C, D)), z)",
"Equals(LengthOf(Line(B, D)), \\sqrt{2})",
"Equals(LengthOf(Line(B, C)), y)",
"Equals(LengthOf(Line(A, B)), x)",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(C, D), Line(B, D))",
"Perpendicular(Line(B, C), Line(A, ... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 0.0], "B": [224.0, 178.0], "C": [365.0, 0.0], "D": [222.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, O, E)), 45)
- PointLiesOnLine(O, Line(A, B))
- PointLiesOnLine(O, Line(E, C))
- PointLiesOnCircle(A, Circle(O, radius_1_0))
- PointLiesOnCircle(C, Circle(O, radius_1_0))
- PointLiesOnCircle(F, Circle(O, radius_1_0))
- PointLiesOnCircle(E, Circle(O, radius_1_0))
- PointLie... | 270 | [
"IsDiameterOf(Line(E,C),Circle(O))",
"IsDiameterOf(Line(A,B),Circle(O))",
"Find(MeasureOf(Arc(A,C,E)))"
] | [
"Equals(MeasureOf(Angle(F, O, E)), 45)",
"PointLiesOnLine(O, Line(A, B))",
"PointLiesOnLine(O, Line(E, C))",
"PointLiesOnCircle(A, Circle(O, radius_1_0))",
"PointLiesOnCircle(C, Circle(O, radius_1_0))",
"PointLiesOnCircle(F, Circle(O, radius_1_0))",
"PointLiesOnCircle(E, Circle(O, radius_1_0))",
"Poin... | [
"AB",
"AO",
"CE",
"OB",
"OC",
"OE",
"OF"
] | {"A": [32.0, 180.0], "B": [181.0, 31.0], "C": [179.0, 180.0], "E": [31.0, 31.0], "F": [1.0, 109.0], "O": [105.0, 104.0]} | [
"O"
] |
Diagram Logic Form:
- PointLiesOnLine(O, Line(E, C))
- PointLiesOnLine(O, Line(A, B))
- PointLiesOnCircle(E, Circle(O, radius_0_0))
- PointLiesOnCircle(F, Circle(O, radius_0_0))
- PointLiesOnCircle(A, Circle(O, radius_0_0))
- PointLiesOnCircle(C, Circle(O, radius_0_0))
- PointLiesOnCircle(D, Circle(O, radius_0_0))
- Po... | 180 | [
"Circle(O)",
"IsDiameterOf(Line(E,C),Circle(O))",
"IsDiameterOf(Line(A,B),Circle(O))",
"Equals(Angle(B,O,D),Angle(D,O,E))",
"Equals(Angle(D,O,E),Angle(E,O,F))",
"Equals(Angle(E,O,F),Angle(F,O,A))",
"Find(MeasureOf(Arc(A,C,B)))"
] | [
"PointLiesOnLine(O, Line(E, C))",
"PointLiesOnLine(O, Line(A, B))",
"PointLiesOnCircle(E, Circle(O, radius_0_0))",
"PointLiesOnCircle(F, Circle(O, radius_0_0))",
"PointLiesOnCircle(A, Circle(O, radius_0_0))",
"PointLiesOnCircle(C, Circle(O, radius_0_0))",
"PointLiesOnCircle(D, Circle(O, radius_0_0))",
... | [
"AB",
"CE",
"OA",
"OB",
"OC",
"OD",
"OE",
"OF"
] | {"A": [28.0, 147.0], "B": [139.0, 29.0], "C": [146.0, 144.0], "D": [82.0, 2.0], "E": [26.0, 28.0], "F": [2.0, 89.0], "O": [85.0, 85.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), x-1)
- Equals(LengthOf(Line(C, E)), x+2)
- Equals(LengthOf(Line(E, F)), 8)
- Equals(LengthOf(Line(B, A)), 3)
- PointLiesOnLine(C, Line(D, B))
- PointLiesOnLine(G, Line(D, A))
- PointLiesOnLine(D, Line(B, E))
- PointLiesOnLine(C, Line(B, E))
- PointLiesOnLine(D, Line(E,... | 1.8 | [
"Find(LengthOf(Line(B,D)))"
] | [
"Equals(LengthOf(Line(B, D)), x-1)",
"Equals(LengthOf(Line(C, E)), x+2)",
"Equals(LengthOf(Line(E, F)), 8)",
"Equals(LengthOf(Line(B, A)), 3)",
"PointLiesOnLine(C, Line(D, B))",
"PointLiesOnLine(G, Line(D, A))",
"PointLiesOnLine(D, Line(B, E))",
"PointLiesOnLine(C, Line(B, E))",
"PointLiesOnLine(D, ... | [
"AG",
"BA",
"BC",
"BE",
"CF",
"CG",
"DA",
"DB",
"DC",
"DE",
"DG",
"EC",
"EF",
"GF"
] | {"A": [1.0, 129.0], "B": [2.0, 205.0], "C": [62.0, 206.0], "D": [245.0, 206.0], "E": [381.0, 207.0], "F": [381.0, 1.0], "G": [122.0, 167.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(A, Line(D, B))
- PointLiesOnLine(C, Line(D, G))
- PointLiesOnLine(C, Line(D, E))
- PointLiesOnLine(G, Line(B, F))
- PointLiesOnLine(G, Line(D, E))
- PointLiesOnLine(G, Line(C, E))
- PointLiesOnCircle(A, Circle(O, radius_4_0))
- PointLiesOnCircle(C, Circle(O, radius_4_0))
- PointLie... | 30 | [
"Equals(MeasureOf(Arc(F,E)),118)",
"Equals(MeasureOf(Arc(A,B)),108)",
"Equals(MeasureOf(Angle(E,G,B)),52)",
"Equals(MeasureOf(Angle(E,F,B)),30)",
"Find(MeasureOf(Arc(A,C)))"
] | [
"PointLiesOnLine(A, Line(D, B))",
"PointLiesOnLine(C, Line(D, G))",
"PointLiesOnLine(C, Line(D, E))",
"PointLiesOnLine(G, Line(B, F))",
"PointLiesOnLine(G, Line(D, E))",
"PointLiesOnLine(G, Line(C, E))",
"PointLiesOnCircle(A, Circle(O, radius_4_0))",
"PointLiesOnCircle(C, Circle(O, radius_4_0))",
"P... | [
"AD",
"DB",
"BD",
"DC",
"DG",
"DE",
"CG",
"CE",
"GE",
"EF"
] | {"A": [149.0, 30.0], "B": [265.0, 32.0], "C": [137.0, 65.0], "D": [0.0, 28.0], "E": [269.0, 100.0], "F": [153.0, 115.0], "G": [197.0, 82.0], "O": [205.0, 78.0]} | [
"O"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 56)
The diagonals of rectangle $A B C D$ each have a length of 56 feet. If $m \angle B A C=42^{\circ}$, what is the length of $\overline{A B}$ to the nearest tenth of a foot? | 41.6 | [
"Rectangle(A,B,C,D)",
"IsDiagonalOf(Line(A,C),Rectangle(A,B,C,D))",
"IsDiagonalOf(Line(B,D),Rectangle(A,B,C,D))",
"Equals(LengthOf(Line(A,C)),56)",
"Equals(LengthOf(Line(B,D)),56)",
"Equals(MeasureOf(Angle(B,A,C)),42)",
"Find(LengthOf(Line(A,B)))"
] | [
"Equals(LengthOf(Line(B, D)), 56)"
] | [
"AB",
"BC",
"CD",
"AD",
"BD"
] | {"A": [0.0, 0.0], "B": [300.0, 1.0], "C": [301.0, 108.0], "D": [1.0, 108.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(P, Q))
- PointLiesOnLine(S, Line(P, R))
- Parallel(Line(T, S), Line(Q, R))
In $\triangle PQR$, $\overline{ST} \| \overline{R Q}$ . If $PT=7.5$, $TQ=3$, and $SR=2.5$, find $PS$. | 6.25 | [
"Triangle(P,Q,R)",
"Parallel(Line(S,T),Line(R,Q))",
"Equals(LengthOf(Line(P,T)),7.5)",
"Equals(LengthOf(Line(T,Q)),3)",
"Equals(LengthOf(Line(S,R)),2.5)",
"Find(LengthOf(Line(P,S)))"
] | [
"PointLiesOnLine(T, Line(P, Q))",
"PointLiesOnLine(S, Line(P, R))",
"Parallel(Line(T, S), Line(Q, R))"
] | [
"PQ",
"PR",
"PS",
"PT",
"QR",
"QT",
"RS",
"TS"
] | {"P": [104.0, 0.0], "Q": [405.0, 235.0], "R": [1.0, 312.0], "S": [29.0, 228.0], "T": [323.0, 170.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, X)), 2x+1)
- Equals(LengthOf(Line(B, C)), 7)
- Equals(LengthOf(Line(D, X)), 15)
- Equals(LengthOf(Line(B, D)), x)
- PointLiesOnLine(B, Line(C, D))
- Equals(MeasureOf(Angle(C, X, B)), MeasureOf(Angle(B, X, D)))
Find x | 7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, X)), 2x+1)",
"Equals(LengthOf(Line(B, C)), 7)",
"Equals(LengthOf(Line(D, X)), 15)",
"Equals(LengthOf(Line(B, D)), x)",
"PointLiesOnLine(B, Line(C, D))",
"Equals(MeasureOf(Angle(C, X, B)), MeasureOf(Angle(B, X, D)))"
] | [
"BC",
"BD",
"BX",
"CD",
"CX",
"DX"
] | {"B": [132.0, 106.0], "C": [0.0, 10.0], "D": [260.0, 198.0], "X": [245.0, -2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, C)), 8)
Find the area of the regular polygon. Round to the nearest tenth. | 212.1 | [
"Find(AreaOf(Regular(Polygon($))))"
] | [
"Equals(LengthOf(Line(F, C)), 8)"
] | [
"AG",
"AJ",
"BE",
"BH",
"CF",
"CI",
"GE",
"HD",
"ID",
"JC",
"JI"
] | {"A": [2.0, 149.0], "B": [149.0, 2.0], "C": [103.0, 209.0], "D": [209.0, 147.0], "E": [62.0, 1.0], "F": [104.0, 100.0], "G": [1.0, 61.0], "H": [208.0, 60.0], "I": [147.0, 209.0], "J": [62.0, 208.0]} | [
""
] |
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 scale factor of $▱ F G H J$ to $▱ A B C D$. | \frac { 3 } { 5 } | [
"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(ScaleFactorOf(Parallelogram(F,G,H,J),Parallelogram(A,B,C,D)))"
] | [
"Equals(LengthOf(Line(C, D)), 10)",
"Equals(LengthOf(Line(J, H)), x)"
] | [
"BC",
"BA",
"CD",
"AD",
"FG",
"GH",
"JH",
"FJ"
] | {"B": [144.0, 1.0], "C": [109.0, 165.0], "A": [35.0, 2.0], "D": [2.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, N, C)), 2x+1)
- Equals(MeasureOf(Angle(E, N, D)), 5x+5)
- Equals(MeasureOf(Angle(B, E, C)), y^2)
- Equals(MeasureOf(Angle(B, D, C)), 3y+10)
- PointLiesOnLine(E, Line(D, B))
- PointLiesOnLine(E, Line(C, N))
- PointLiesOnLine(G, Line(E, F))
Quadrilateral ABCD is a rectangl... | 5 | [
"Rectangle(A,B,C,D)",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(B, N, C)), 2x+1)",
"Equals(MeasureOf(Angle(E, N, D)), 5x+5)",
"Equals(MeasureOf(Angle(B, E, C)), y^2)",
"Equals(MeasureOf(Angle(B, D, C)), 3y+10)",
"PointLiesOnLine(E, Line(D, B))",
"PointLiesOnLine(E, Line(C, N))",
"PointLiesOnLine(G, Line(E, F))"
] | [
"BC",
"BE",
"BF",
"BG",
"BN",
"CE",
"CN",
"DB",
"DC",
"DE",
"DG",
"DN",
"EF",
"EG",
"GF",
"NE"
] | {"B": [325.0, 2.0], "C": [325.0, 150.0], "D": [1.0, 149.0], "E": [163.0, 75.0], "F": [288.0, 8.0], "G": [266.0, 20.0], "N": [1.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, D, A)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(A, D, E)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(H, E, B)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(I, D, H)), MeasureOf(angle 8))
- Equals(MeasureOf(A... | 57 | [
"Parallel(Line(a),Line(b))",
"Parallel(Line(c),Line(d))",
"Equals(MeasureOf(Angle(4)),57)",
"Find(MeasureOf(Angle(8)))"
] | [
"Equals(MeasureOf(Angle(H, D, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(A, D, E)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(H, E, B)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(B, E, C)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(I, D, H)), MeasureOf(angle 8))",
"Equals(MeasureOf(Ang... | [
"DE",
"DH",
"DC",
"DI",
"DA",
"DL",
"EG",
"EH",
"EC",
"EK",
"EB",
"HC",
"IF",
"IJ",
"IK",
"IA",
"IL",
"AL",
"GK",
"GB",
"KF",
"KJ",
"KB",
"FJ"
] | {"D": [207.542468791765, 45.269343418545816], "E": [353.10239713367645, 45.65544402422728], "F": [0.0, 141.0], "G": [192.0, 187.0], "H": [106.0, 45.0], "C": [483.0, 46.0], "J": [377.0, 141.0], "I": [98.43010752688173, 141.0], "K": [244.43010752688173, 141.0], "B": [404.0, 1.0], "A": [258.0, 1.0], "L": [46.0, 187.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, K)), 2z+7)
- Equals(LengthOf(Line(J, N)), 3y-5)
- Equals(LengthOf(Line(L, N)), y+5)
- Equals(LengthOf(Line(N, M)), z+9)
- PointLiesOnLine(N, Line(L, J))
- PointLiesOnLine(N, Line(M, K))
Use parallelogram to find $y$ | 5 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(N, K)), 2z+7)",
"Equals(LengthOf(Line(J, N)), 3y-5)",
"Equals(LengthOf(Line(L, N)), y+5)",
"Equals(LengthOf(Line(N, M)), z+9)",
"PointLiesOnLine(N, Line(L, J))",
"PointLiesOnLine(N, Line(M, K))"
] | [
"JK",
"JN",
"KN",
"LJ",
"LK",
"LM",
"LN",
"MJ",
"MK",
"MN"
] | {"J": [84.0, 36.0], "K": [416.0, 1.0], "L": [327.0, 213.0], "M": [2.0, 250.0], "N": [208.0, 126.0]} | [
""
] |
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, ... | 70 | [
"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,I)))"
] | [
"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:
- Equals(MeasureOf(Angle(E, A, F)), x)
- Equals(MeasureOf(Angle(D, A, E)), 3x)
- Equals(MeasureOf(Angle(B, A, C)), 2x)
- PointLiesOnLine(F, Line(A, B))
- PointLiesOnLine(A, Line(C, D))
Find x | 30 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, A, F)), x)",
"Equals(MeasureOf(Angle(D, A, E)), 3x)",
"Equals(MeasureOf(Angle(B, A, C)), 2x)",
"PointLiesOnLine(F, Line(A, B))",
"PointLiesOnLine(A, Line(C, D))"
] | [
"AB",
"AC",
"AD",
"AE",
"AF",
"BF",
"CD"
] | {"A": [90.49752481688037, 134.29493541111339], "B": [156.0, 24.5], "C": [237.0, 135.0], "D": [0.0, 135.0], "E": [90.0, 0.0], "F": [140.13636363636363, 48.814935064935064]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 12)
- Equals(LengthOf(Line(C, F)), 6)
- Equals(LengthOf(Line(B, D)), x)
- Equals(LengthOf(Line(E, F)), y)
- Equals(LengthOf(Line(A, E)), 3)
- Equals(LengthOf(Line(E, H)), 2)
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(F, Line(A, C))
- PointLiesOnLine(E, Line(A, ... | 15 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), 12)",
"Equals(LengthOf(Line(C, F)), 6)",
"Equals(LengthOf(Line(B, D)), x)",
"Equals(LengthOf(Line(E, F)), y)",
"Equals(LengthOf(Line(A, E)), 3)",
"Equals(LengthOf(Line(E, H)), 2)",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(F, Line(A, C))",
"PointLiesOnLine(E, L... | [
"AC",
"AE",
"AF",
"AH",
"BD",
"CB",
"CE",
"CF",
"EB",
"ED",
"EF",
"EH",
"HB",
"HD"
] | {"A": [66.0, 169.0], "B": [84.0, 2.0], "C": [170.0, 0.0], "D": [90.0, 86.0], "E": [87.0, 135.0], "F": [152.0, 29.0], "H": [88.0, 171.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(U, J)), 9)
- Equals(LengthOf(Line(J, V)), 3)
- PointLiesOnLine(V, Line(Z, U))
- PointLiesOnLine(Y, Line(Z, S))
- PointLiesOnLine(J, Line(Z, T))
- PointLiesOnLine(J, Line(U, Y))
- PointLiesOnLine(T, Line(U, S))
- PointLiesOnLine(J, Line(S, V))
- Equals(LengthOf(Line(S, T)), Len... | 12 | [
"Equals(LengthOf(Line(U,J)),9)",
"Equals(LengthOf(Line(V,J)),3)",
"Equals(LengthOf(Line(Z,T)),18)",
"Find(LengthOf(Line(Z,J)))"
] | [
"Equals(LengthOf(Line(U, J)), 9)",
"Equals(LengthOf(Line(J, V)), 3)",
"PointLiesOnLine(V, Line(Z, U))",
"PointLiesOnLine(Y, Line(Z, S))",
"PointLiesOnLine(J, Line(Z, T))",
"PointLiesOnLine(J, Line(U, Y))",
"PointLiesOnLine(T, Line(U, S))",
"PointLiesOnLine(J, Line(S, V))",
"Equals(LengthOf(Line(S, T... | [
"JS",
"JT",
"JV",
"JY",
"ST",
"SV",
"UJ",
"US",
"UT",
"UV",
"UY",
"YS",
"ZJ",
"ZS",
"ZT",
"ZU",
"ZV",
"ZY"
] | {"J": [197.0, 164.0], "S": [27.0, 2.0], "T": [287.0, 60.0], "U": [546.0, 119.0], "V": [282.0, 245.0], "Y": [21.0, 186.0], "Z": [14.0, 372.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 3.6)
- Equals(LengthOf(Line(D, C)), 2)
- Equals(LengthOf(Line(A, B)), 6)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(C, D), Line(B, D))
Find the area of the triangle. Round to the nearest tenth if necessary. | 6 | [
"Find(AreaOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, C)), 3.6)",
"Equals(LengthOf(Line(D, C)), 2)",
"Equals(LengthOf(Line(A, B)), 6)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(C, D), Line(B, D))"
] | [
"AB",
"AC",
"BC"
] | {"A": [214.0, 114.0], "B": [0.0, 115.0], "C": [108.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, C)), 12)
- Equals(LengthOf(Line(H, I)), x)
- Equals(AreaOf(Rectangle(A, B, E, C)), 72)
- Equals(AreaOf(Rectangle(F, G, H, I)), 50)
For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. | \frac { 6 } { 5 } | [
"Similar(Shape($1),Shape($2))",
"Find(ScaleFactorOf(Blue(Shape($)),Green(Shape($))))"
] | [
"Equals(LengthOf(Line(E, C)), 12)",
"Equals(LengthOf(Line(H, I)), x)",
"Equals(AreaOf(Rectangle(A, B, E, C)), 72)",
"Equals(AreaOf(Rectangle(F, G, H, I)), 50)"
] | [
"BA",
"CA",
"EB",
"EC"
] | {"A": [1.0, 0.0], "B": [125.0, 2.0], "C": [0.0, 69.0], "E": [127.0, 69.0]} | [
""
] |
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... | 3 | [
"Find(x)"
] | [
"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(Q, Line(N, K))
- PointLiesOnLine(Q, Line(M, J))
- Perpendicular(Line(K, J), Line(N, J))
- Perpendicular(Line(K, M), Line(M, N))
$JKMN$ is a rectangle. If $NQ=2x+3$ and $QK=5x-9$, find $JQ$. | 11 | [
"Rectangle(J,K,M,N)",
"Equals(LengthOf(Line(N,Q)),2x+3)",
"Equals(LengthOf(Line(Q,K)),5x-9)",
"Find(LengthOf(Line(J,Q)))"
] | [
"PointLiesOnLine(Q, Line(N, K))",
"PointLiesOnLine(Q, Line(M, J))",
"Perpendicular(Line(K, J), Line(N, J))",
"Perpendicular(Line(K, M), Line(M, N))"
] | [
"JQ",
"KJ",
"KM",
"KQ",
"MJ",
"MQ",
"NJ",
"NK",
"NM",
"NQ"
] | {"J": [2.0, 0.0], "K": [446.0, 2.0], "M": [449.0, 230.0], "N": [2.0, 230.0], "Q": [225.0, 116.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 5)
- Equals(LengthOf(Line(C, D)), 12)
- Equals(LengthOf(Line(C, B)), 31.2)
- PointLiesOnLine(D, Line(B, A))
- Perpendicular(Line(B, D), Line(C, D))
- Perpendicular(Line(C, D), Line(C, B))
Find the perimeter of the $\triangle A B C,$ if $\triangle A B C \sim \triangle ... | 78 | [
"Similar(Triangle(A,B,C),Triangle(C,B,D))",
"Equals(LengthOf(Line(A,D)),5)",
"Equals(LengthOf(Line(C,D)),12)",
"Equals(LengthOf(Line(B,C)),31.2)",
"Find(PerimeterOf(Triangle(A,B,C)))"
] | [
"Equals(LengthOf(Line(A, D)), 5)",
"Equals(LengthOf(Line(C, D)), 12)",
"Equals(LengthOf(Line(C, B)), 31.2)",
"PointLiesOnLine(D, Line(B, A))",
"Perpendicular(Line(B, D), Line(C, D))",
"Perpendicular(Line(C, D), Line(C, B))"
] | [
"AD",
"BA",
"BD",
"CA",
"CB",
"CD"
] | {"A": [0.0, 0.0], "B": [413.0, 1.0], "C": [62.0, 148.0], "D": [60.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, C)), 27)
- Equals(LengthOf(Line(A, D)), 62)
- Equals(LengthOf(Line(A, O)), 54)
- PointLiesOnLine(F, Line(B, O))
- Perpendicular(Line(A, D), Line(A, E))
- Perpendicular(Line(C, F), Line(B, F))
Find the area of the figure. Round to the nearest tenth if necessary. | 4185 | [
"Find(AreaOf(Shape($)))"
] | [
"Equals(LengthOf(Line(F, C)), 27)",
"Equals(LengthOf(Line(A, D)), 62)",
"Equals(LengthOf(Line(A, O)), 54)",
"PointLiesOnLine(F, Line(B, O))",
"Perpendicular(Line(A, D), Line(A, E))",
"Perpendicular(Line(C, F), Line(B, F))"
] | [
"AD",
"AO",
"BC",
"DB",
"OC",
"BF",
"CF",
"OF",
"BO"
] | {"A": [1.0, 180.0], "B": [156.0, 2.0], "C": [233.0, 90.0], "D": [1.0, 0.0], "O": [156.0, 178.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(M, L, P)), 31)
- Equals(MeasureOf(Angle(L, N, M)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(P, N, Q)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(N, Q, P)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(Q, P, N)), 22)
- PointLiesOnLine(N, Line(L, P))
- PointLiesOnLine(N... | 59 | [
"Find(MeasureOf(Angle(1)))"
] | [
"Equals(MeasureOf(Angle(M, L, P)), 31)",
"Equals(MeasureOf(Angle(L, N, M)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(P, N, Q)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(N, Q, P)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(Q, P, N)), 22)",
"PointLiesOnLine(N, Line(L, P))",
"PointLiesOnLine(... | [
"LM",
"LN",
"LP",
"MQ",
"NM",
"NQ",
"PN",
"PQ"
] | {"L": [0.0, 0.0], "M": [287.0, 1.0], "N": [287.0, 173.0], "P": [529.0, 318.0], "Q": [286.0, 281.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(E, Line(B, D))
ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find $m\angle BDA$ | 55 | [
"Rhombus(A,B,C,D)",
"Equals(LengthOf(Line(E,B)),9)",
"Equals(LengthOf(Line(A,B)),12)",
"Equals(MeasureOf(Angle(A,B,D)),55)",
"Find(MeasureOf(Angle(B,D,A)))"
] | [
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(E, Line(B, D))"
] | [
"EA",
"EC",
"EB",
"ED",
"AC",
"AB",
"AD",
"CB",
"CD",
"BD"
] | {"E": [160.05631466857648, 113.92265214195517], "A": [1.099114777678551, 17.453155634667112], "C": [320.54726647843233, 213.2402434543077], "B": [243.1611090480451, 0.026497646449143986], "D": [78.45017421921474, 225.77639322137333]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Y, Q, F)), 4x-5)
- Equals(MeasureOf(Angle(E, Y, Q)), 3y+1)
- Equals(MeasureOf(Angle(M, A, Q)), 3x+11)
- PointLiesOnLine(Y, Line(E, M))
- PointLiesOnLine(Q, Line(F, A))
- Parallel(Line(E, F), Line(Y, Q))
- Parallel(Line(Y, Q), Line(M, A))
- Parallel(Line(M, A), Line(E, F))
- ... | 40 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(Y, Q, F)), 4x-5)",
"Equals(MeasureOf(Angle(E, Y, Q)), 3y+1)",
"Equals(MeasureOf(Angle(M, A, Q)), 3x+11)",
"PointLiesOnLine(Y, Line(E, M))",
"PointLiesOnLine(Q, Line(F, A))",
"Parallel(Line(E, F), Line(Y, Q))",
"Parallel(Line(Y, Q), Line(M, A))",
"Parallel(Line(M, A), Line(E, F)... | [
"",
"AF",
"AM",
"EF",
"EM",
"EY",
"FQ",
"QA",
"YM",
"YQ"
] | {"A": [378.0, 120.0], "E": [1.0, 8.0], "F": [311.0, 7.0], "M": [66.0, 119.0], "Q": [345.0, 66.0], "Y": [37.0, 67.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(Z, Y, X)), 120)
- Perpendicular(Line(W, X), Line(Z, W))
If WXYZ is a kite, find $m\angle Z$ | 75 | [
"Kite(W,X,Y,Z)",
"Find(MeasureOf(Angle(Z)))"
] | [
"Equals(MeasureOf(Angle(Z, Y, X)), 120)",
"Perpendicular(Line(W, X), Line(Z, W))"
] | [
"WX",
"YX",
"ZW",
"ZY"
] | {"W": [98.0, 151.0], "X": [0.0, 56.0], "Y": [99.0, 1.0], "Z": [189.0, 54.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), 18)
- Equals(LengthOf(Line(A, B)), 24)
- Equals(LengthOf(Line(C, D)), 2x+1)
- Equals(LengthOf(Line(A, C)), 3x-1)
- PointLiesOnLine(D, Line(B, C))
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(D, A, C)))
Find $x$. | 7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, D)), 18)",
"Equals(LengthOf(Line(A, B)), 24)",
"Equals(LengthOf(Line(C, D)), 2x+1)",
"Equals(LengthOf(Line(A, C)), 3x-1)",
"PointLiesOnLine(D, Line(B, C))",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(D, A, C)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 282.0], "B": [253.0, 3.0], "C": [254.0, 315.0], "D": [254.0, 192.0]} | [
""
] |
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 $m\angle T$ | 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(LengthOf(Line(L, O)), 10)
- Equals(LengthOf(Line(L, M)), 8)
- Equals(LengthOf(Line(M, N)), 16)
- Equals(LengthOf(Line(D, B)), 12)
- Equals(LengthOf(Line(A, F)), y+1)
- Equals(LengthOf(Line(A, D)), x-3)
- Perpendicular(Line(A, D), Line(D, B))
- Perpendicular(Line(D, B), Line(B, F))
- Perpend... | 27 | [
"Similar(Polygon($1),Polygon($2))",
"Find(x)"
] | [
"Equals(LengthOf(Line(L, O)), 10)",
"Equals(LengthOf(Line(L, M)), 8)",
"Equals(LengthOf(Line(M, N)), 16)",
"Equals(LengthOf(Line(D, B)), 12)",
"Equals(LengthOf(Line(A, F)), y+1)",
"Equals(LengthOf(Line(A, D)), x-3)",
"Perpendicular(Line(A, D), Line(D, B))",
"Perpendicular(Line(D, B), Line(B, F))",
"... | [
"AF",
"BD",
"DA",
"FB",
"LM",
"MN",
"NO",
"OL"
] | {"A": [309.0, 201.0], "B": [1.0, 16.0], "D": [1.0, 200.0], "F": [210.0, 18.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(S, T)), 12+x)
- Equals(LengthOf(Line(S, R)), 4x-4)
- Equals(LengthOf(Line(R, T)), 3x+3)
- Equals(LengthOf(Line(S, R)), LengthOf(Line(R, T)))
Find $SR$. | 24 | [
"Find(LengthOf(Line(R,T)))"
] | [
"Equals(LengthOf(Line(S, T)), 12+x)",
"Equals(LengthOf(Line(S, R)), 4x-4)",
"Equals(LengthOf(Line(R, T)), 3x+3)",
"Equals(LengthOf(Line(S, R)), LengthOf(Line(R, T)))"
] | [
"SR",
"ST",
"RT"
] | {"S": [0.0, 0.0], "R": [98.14848484848484, 219.25775941230486], "T": [196.03755192256392, 1.3269463816165512]} | [] |
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