problem stringlengths 75 15.2k | answer stringlengths 1 34 | text_logic_form listlengths 1 11 | diagram_logic_form listlengths 0 456 | line_instances listlengths 1 110 | point_positions stringlengths 2 551 | circle_instances listlengths 0 4 |
|---|---|---|---|---|---|---|
Diagram Logic Form:
- Equals(LengthOf(Line(C, F)), x)
- Equals(LengthOf(Line(F, D)), 6)
- Equals(LengthOf(Line(F, E)), 4)
- Equals(LengthOf(Line(B, F)), 8)
- PointLiesOnLine(F, Line(B, C))
- PointLiesOnLine(F, Line(E, D))
- PointLiesOnCircle(B, Circle(A, radius_0_0))
- PointLiesOnCircle(C, Circle(A, radius_0_0))
- Poin... | 3 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, F)), x)",
"Equals(LengthOf(Line(F, D)), 6)",
"Equals(LengthOf(Line(F, E)), 4)",
"Equals(LengthOf(Line(B, F)), 8)",
"PointLiesOnLine(F, Line(B, C))",
"PointLiesOnLine(F, Line(E, D))",
"PointLiesOnCircle(B, Circle(A, radius_0_0))",
"PointLiesOnCircle(C, Circle(A, radius_0_0))",
... | [
"BC",
"BF",
"CE",
"CF",
"ED",
"FD",
"FE"
] | {"A": [116.0, 115.0], "B": [214.0, 172.0], "C": [60.0, 14.0], "D": [222.0, 75.0], "E": [21.0, 50.0], "F": [105.0, 61.0]} | [
"A"
] |
Diagram Logic Form:
- PointLiesOnLine(N, Line(D, A))
- PointLiesOnCircle(D, Circle(N, radius_0_0))
- PointLiesOnCircle(A, Circle(N, radius_0_0))
- PointLiesOnCircle(B, Circle(N, radius_0_0))
- PointLiesOnCircle(C, Circle(N, radius_0_0))
- PointLiesOnCircle(E, Circle(N, radius_0_0))
If $\overline{B E} \cong \overline{E... | 120 | [
"Equals(LengthOf(Line(B,E)),Line(E,D))",
"Equals(MeasureOf(Arc(E,D)),120)",
"Find(MeasureOf(Arc(B,E)))"
] | [
"PointLiesOnLine(N, Line(D, A))",
"PointLiesOnCircle(D, Circle(N, radius_0_0))",
"PointLiesOnCircle(A, Circle(N, radius_0_0))",
"PointLiesOnCircle(B, Circle(N, radius_0_0))",
"PointLiesOnCircle(C, Circle(N, radius_0_0))",
"PointLiesOnCircle(E, Circle(N, radius_0_0))"
] | [
"BC",
"DA",
"DE",
"NA",
"NB",
"NC",
"ND"
] | {"A": [13.0, 25.0], "B": [80.0, 8.0], "C": [109.0, 28.0], "D": [115.0, 102.0], "E": [20.0, 96.0], "N": [66.0, 63.0]} | [
"N"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(B, C)), 22)
- Equals(LengthOf(Line(A, C)), 20)
- Perpendicular(Line(B, C), Line(A, C))
Find x. | 2 \sqrt { 221 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, C)), 22)",
"Equals(LengthOf(Line(A, C)), 20)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [197.42274978466838, 216.00247631352283], "B": [0.6666666666666572, 0.6984924623115489], "C": [0.6666666666666572, 217.32994923857868]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, B, N)), 2x+45)
- Equals(LengthOf(Line(E, F)), x)
- Equals(MeasureOf(Angle(A, E, D)), 3x)
- PointLiesOnLine(E, Line(A, T))
- PointLiesOnLine(B, Line(E, F))
- PointLiesOnLine(E, Line(B, D))
- PointLiesOnLine(B, Line(C, N))
- PointLiesOnLine(B, Line(D, F))
- PointLiesOnLine(... | 27 | [
"Parallel(Line(m),Line(n))",
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, B, N)), 2x+45)",
"Equals(LengthOf(Line(E, F)), x)",
"Equals(MeasureOf(Angle(A, E, D)), 3x)",
"PointLiesOnLine(E, Line(A, T))",
"PointLiesOnLine(B, Line(E, F))",
"PointLiesOnLine(E, Line(B, D))",
"PointLiesOnLine(B, Line(C, N))",
"PointLiesOnLine(B, Line(D, F))",
"PointLies... | [
"AE",
"AT",
"BC",
"BD",
"BF",
"BN",
"CN",
"DF",
"EB",
"ED",
"EF",
"TE"
] | {"A": [92.0, 259.0], "B": [286.0, 102.0], "C": [279.0, 258.0], "D": [0.0, 200.0], "E": [92.0, 168.0], "F": [327.0, 88.0], "N": [290.0, 5.0], "T": [92.0, 1.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(E, Line(D, A))
- PointLiesOnLine(B, Line(D, A))
- PointLiesOnLine(B, Line(D, E))
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnLine(D, Line(A, C))
- PointLiesOnLine(E, Line(A, C))
- PointLiesOnLine(B, Line(A, C))
- PointLiesOnLine(D, Line(E, C))
- PointLiesOnLine(B, Line(E, C))
- P... | 27 | [
"Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(B)),2))",
"Equals(RadiusOf(Circle(A)),Mul(RadiusOf(Circle(C)),4))",
"Equals(SumOf(CircumferenceOf(Circle($1)),CircumferenceOf(Circle($2)),CircumferenceOf(Circle($3))),42\\pi)",
"Find(LengthOf(Line(A,C)))"
] | [
"PointLiesOnLine(E, Line(D, A))",
"PointLiesOnLine(B, Line(D, A))",
"PointLiesOnLine(B, Line(D, E))",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnLine(D, Line(A, C))",
"PointLiesOnLine(E, Line(A, C))",
"PointLiesOnLine(B, Line(A, C))",
"PointLiesOnLine(D, Line(E, C))",
"PointLiesOnLine(B, Line(E, ... | [
"AB",
"AC",
"AE",
"BC",
"DA",
"DB",
"DC",
"DE",
"EB",
"EC"
] | {"A": [268.0, 104.0], "B": [109.0, 105.0], "C": [27.0, 103.0], "D": [57.0, 102.0], "E": [161.0, 103.0]} | [
"A",
"B",
"C"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, D, A)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(B, C, A)), 42)
- Equals(MeasureOf(Angle(A, B, C)), 38)
- Equals(MeasureOf(Angle(A, D, C)), 72)
- Equals(MeasureOf(Angle(D, A, B)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 3))
- PointLiesO... | 34 | [
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(B, D, A)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(B, C, A)), 42)",
"Equals(MeasureOf(Angle(A, B, C)), 38)",
"Equals(MeasureOf(Angle(A, D, C)), 72)",
"Equals(MeasureOf(Angle(D, A, B)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(C, A, D)), MeasureOf(angle 3))",
"PointLies... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [202.0, 184.0], "B": [434.0, 2.0], "C": [-0.0, 1.0], "D": [262.0, 2.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, H)), a)
- Equals(LengthOf(Line(A, F)), 12)
- Equals(LengthOf(Line(D, G)), 12)
- Equals(LengthOf(Line(A, D)), 12)
- Equals(LengthOf(Line(D, H)), 6)
- Equals(MeasureOf(Angle(G, D, H)), 60)
- PointLiesOnLine(H, Line(A, D))
- Perpendicular(Line(G, H), Line(D, H))
Find the area... | 374.1 | [
"Equals(PerimeterOf(Regular(Hexagon($))),72)",
"Find(AreaOf(Regular(Hexagon($))))"
] | [
"Equals(LengthOf(Line(G, H)), a)",
"Equals(LengthOf(Line(A, F)), 12)",
"Equals(LengthOf(Line(D, G)), 12)",
"Equals(LengthOf(Line(A, D)), 12)",
"Equals(LengthOf(Line(D, H)), 6)",
"Equals(MeasureOf(Angle(G, D, H)), 60)",
"PointLiesOnLine(H, Line(A, D))",
"Perpendicular(Line(G, H), Line(D, H))"
] | [
"AD",
"AE",
"AF",
"AG",
"AH",
"DB",
"DC",
"DG",
"DH",
"EB",
"EC",
"FC",
"GH"
] | {"A": [57.0, 192.0], "B": [221.0, 97.0], "C": [55.0, 2.0], "D": [166.0, 191.0], "E": [167.0, 2.0], "F": [2.0, 96.0], "G": [111.0, 104.0], "H": [113.0, 192.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(O, B)), 20)
- Equals(LengthOf(Line(A, C)), 25)
- Equals(LengthOf(Line(A, N)), 21)
- PointLiesOnLine(N, Line(A, O))
- Perpendicular(Line(B, O), Line(N, O))
Find the area of the parallelogram. Round to the nearest tenth if necessary. | 420 | [
"Find(AreaOf(Parallelogram($)))"
] | [
"Equals(LengthOf(Line(O, B)), 20)",
"Equals(LengthOf(Line(A, C)), 25)",
"Equals(LengthOf(Line(A, N)), 21)",
"PointLiesOnLine(N, Line(A, O))",
"Perpendicular(Line(B, O), Line(N, O))"
] | [
"AC",
"AN",
"AO",
"BO",
"CB",
"NB",
"NO"
] | {"A": [1.0, 137.0], "B": [229.0, 1.0], "C": [93.0, 2.0], "N": [134.0, 137.0], "O": [149.0, 137.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(D, C)), 17)
- Equals(LengthOf(Line(E, C)), 92)
- Equals(LengthOf(Line(D, C)), 92)
- Equals(LengthOf(Line(B, F)), 108)
- Equals(LengthOf(Line(A, D)), 31)
- Equals(LengthOf(Line(F, A)), 31)
Find the area of the shaded region. Round to the nearest tenth if necessary. | 108.5 | [
"Find(AreaOf(Shaded(Shape($))))"
] | [
"Equals(LengthOf(Line(D, C)), 17)",
"Equals(LengthOf(Line(E, C)), 92)",
"Equals(LengthOf(Line(D, C)), 92)",
"Equals(LengthOf(Line(B, F)), 108)",
"Equals(LengthOf(Line(A, D)), 31)",
"Equals(LengthOf(Line(F, A)), 31)"
] | [
"AD",
"BE",
"BF",
"DC",
"EC",
"FA"
] | {"A": [298.0, 139.0], "B": [139.0, 91.0], "C": [0.0, 0.0], "D": [1.0, 138.0], "E": [137.0, 1.0], "F": [299.0, 93.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(I, Line(B, C))
- PointLiesOnCircle(A, Circle(I, radius_8_0))
- PointLiesOnCircle(B, Circle(I, radius_8_0))
- PointLiesOnCircle(C, Circle(I, radius_8_0))
- Perpendicular(Line(A, C), Line(A, B))
- Equals(LengthOf(Line(A, C)), LengthOf(Line(A, B)))
- Equals(LengthOf(Line(A, B)), 6\sqr... | 12 \pi | [
"InscribedIn(Triangle($),Circle($))",
"Find(CircumferenceOf(Circle($)))"
] | [
"PointLiesOnLine(I, Line(B, C))",
"PointLiesOnCircle(A, Circle(I, radius_8_0))",
"PointLiesOnCircle(B, Circle(I, radius_8_0))",
"PointLiesOnCircle(C, Circle(I, radius_8_0))",
"Perpendicular(Line(A, C), Line(A, B))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(A, B)))",
"Equals(LengthOf(Line(A, B)), 6\\s... | [
"AB",
"AC",
"BC",
"BI",
"CI"
] | {"A": [170.0, 4.0], "B": [26.0, 196.0], "C": [362.0, 147.0], "I": [197.0, 172.0]} | [
"I"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), x+3)
- Equals(LengthOf(Line(D, C)), 6)
- Equals(LengthOf(Line(C, A)), 1)
- Equals(LengthOf(Line(E, C)), 11x-2)
- PointLiesOnLine(C, Line(E, B))
- PointLiesOnLine(C, Line(D, A))
Find x | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), x+3)",
"Equals(LengthOf(Line(D, C)), 6)",
"Equals(LengthOf(Line(C, A)), 1)",
"Equals(LengthOf(Line(E, C)), 11x-2)",
"PointLiesOnLine(C, Line(E, B))",
"PointLiesOnLine(C, Line(D, A))"
] | [
"BA",
"CA",
"CB",
"DA",
"DC",
"EB",
"EC",
"ED"
] | {"A": [14.0, 127.0], "B": [0.0, 0.0], "C": [118.0, 78.0], "D": [234.0, 23.0], "E": [250.0, 166.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, J)), 11)
- Equals(MeasureOf(Angle(J, K, L)), 65)
- PointLiesOnCircle(L, Circle(K, radius_0_0))
- PointLiesOnCircle(J, Circle(K, radius_0_0))
Find the area of the shaded sector. Round to the nearest tenth. | 311.5 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(K, J)), 11)",
"Equals(MeasureOf(Angle(J, K, L)), 65)",
"PointLiesOnCircle(L, Circle(K, radius_0_0))",
"PointLiesOnCircle(J, Circle(K, radius_0_0))"
] | [
"KJ",
"KL"
] | {"J": [150.0, 11.0], "K": [103.0, 106.0], "L": [210.0, 106.0]} | [
"K"
] |
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 $x$ in the figure. | 16 | [
"Find(x)"
] | [
"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))",
""
] | [
"GD",
"DC",
"HC",
"HG",
"GC"
] | {"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(MeasureOf(Angle(D, F, E)), 2x)
- Equals(MeasureOf(Angle(C, E, B)), 40)
- Equals(MeasureOf(Angle(D, E, F)), y)
- Equals(MeasureOf(Angle(D, E, F)), Angle(E, D, F))
- PointLiesOnLine(E, Line(F, B))
- PointLiesOnLine(E, Line(C, D))
Find $x$. | 35 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, F, E)), 2x)",
"Equals(MeasureOf(Angle(C, E, B)), 40)",
"Equals(MeasureOf(Angle(D, E, F)), y)",
"Equals(MeasureOf(Angle(D, E, F)), Angle(E, D, F))",
"PointLiesOnLine(E, Line(F, B))",
"PointLiesOnLine(E, Line(C, D))"
] | [
"BC",
"BE",
"CD",
"CE",
"ED",
"FB",
"FD",
"FE"
] | {"B": [357.0, 133.0], "C": [360.0, 3.0], "D": [1.0, 132.0], "E": [181.0, 67.0], "F": [4.0, 2.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(X, Y))
- PointLiesOnLine(R, Line(X, Z))
- PointLiesOnLine(R, Line(Y, W))
- PointLiesOnCircle(X, Circle(R, radius_2_0))
- PointLiesOnCircle(Y, Circle(R, radius_2_0))
- PointLiesOnCircle(W, Circle(R, radius_2_0))
- PointLiesOnCircle(Z, Circle(R, radius_2_0))
- Perpendicular(L... | 90 | [
"InscribedIn(Square(W,X,Y,Z),Circle(R))",
"Find(MeasureOf(Angle($)))"
] | [
"PointLiesOnLine(S, Line(X, Y))",
"PointLiesOnLine(R, Line(X, Z))",
"PointLiesOnLine(R, Line(Y, W))",
"PointLiesOnCircle(X, Circle(R, radius_2_0))",
"PointLiesOnCircle(Y, Circle(R, radius_2_0))",
"PointLiesOnCircle(W, Circle(R, radius_2_0))",
"PointLiesOnCircle(Z, Circle(R, radius_2_0))",
"Perpendicul... | [
"RS",
"WZ",
"XR",
"XS",
"XW",
"XY",
"XZ",
"YR",
"YS",
"YW",
"YZ"
] | {"R": [86.0, 88.0], "S": [149.0, 90.0], "W": [26.0, 28.0], "X": [147.0, 28.0], "Y": [148.0, 151.0], "Z": [26.0, 150.0]} | [
"R"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Y, A)), 8)
- Equals(LengthOf(Line(A, B)), x)
- Perpendicular(Line(A, B), Line(Y, B))
- Equals(LengthOf(Line(A, B)), LengthOf(Line(Y, B)))
Find y. | 45 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(Y, A)), 8)",
"Equals(LengthOf(Line(A, B)), x)",
"Perpendicular(Line(A, B), Line(Y, B))",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(Y, B)))"
] | [
"YA",
"YB",
"AB"
] | {"Y": [239.0, 240.0], "A": [1.0, 0.0], "B": [2.6583676196504484, 238.00411435805466]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, A, D)), 3x)
- Equals(MeasureOf(Angle(A, D, C)), x)
- Perpendicular(Line(B, A), Line(C, B))
- Perpendicular(Line(C, B), Line(C, D))
Find $\angle D$ of quadrilateral ABCD | 45 | [
"Quadrilateral(A,B,C,D)",
"Find(MeasureOf(Angle(D)))"
] | [
"Equals(MeasureOf(Angle(B, A, D)), 3x)",
"Equals(MeasureOf(Angle(A, D, C)), x)",
"Perpendicular(Line(B, A), Line(C, B))",
"Perpendicular(Line(C, B), Line(C, D))"
] | [
"CD",
"CB",
"DA",
"BA"
] | {"C": [399.33517037528145, 180.3341620740618], "D": [0.0, 181.0], "A": [130.5985267034991, 2.0], "B": [399.9944751381215, 2.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(G, F)), 4)
-
- Equals(LengthOf(Line(G, H)), 4)
- Equals(MeasureOf(Angle(F, O, G)), x)
-
- PointLiesOnCircle(H, Circle(O, radius_4_0))
- PointLiesOnCircle(G, Circle(O, radius_4_0))
- PointLiesOnCircle(F, Circle(O, radius_4_0))
Find $x$. | 70 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(G, F)), 4)",
"",
"Equals(LengthOf(Line(G, H)), 4)",
"Equals(MeasureOf(Angle(F, O, G)), x)",
"",
"PointLiesOnCircle(H, Circle(O, radius_4_0))",
"PointLiesOnCircle(G, Circle(O, radius_4_0))",
"PointLiesOnCircle(F, Circle(O, radius_4_0))"
] | [
"GF",
"GH"
] | {"F": [96.0, 9.0], "G": [289.0, 145.0], "H": [93.0, 281.0], "O": [144.0, 146.0]} | [
"O"
] |
Diagram Logic Form:
- PointLiesOnLine(K, Line(G, J))
- PointLiesOnLine(K, Line(H, F))
The diagonals of rhombus FGHJ intersect at K.
If $m\angle FJH = 82$, find $m\angle KHJ$. | 49 | [
"Rhombus(F,G,H,J)",
"IsDiagonalOf(Line(F,H),Rhombus(F,G,H,J))",
"IsDiagonalOf(Line(G,J),Rhombus(F,G,H,J))",
"IntersectAt(Line(F,H),Line(G,J),Point(K))",
"Equals(MeasureOf(Angle(F,J,H)),82)",
"Find(MeasureOf(Angle(K,H,J)))"
] | [
"PointLiesOnLine(K, Line(G, J))",
"PointLiesOnLine(K, Line(H, F))"
] | [
"KG",
"KJ",
"KH",
"KF",
"GJ",
"GH",
"GF",
"JH",
"JF",
"HF"
] | {"K": [67.70719983978104, 96.38158817049968], "G": [100.10869006580022, 0.7673305491067879], "J": [35.853372721431825, 193.00860047182562], "H": [134.8349455483649, 124.3883276204112], "F": [0.19455558364815317, 69.36708578938888]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, Q)), 8)
- Equals(LengthOf(Line(S, T)), y-4)
- Equals(LengthOf(Line(R, Q)), 11)
Find $y$ in the given parallelogram | 15 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(T, Q)), 8)",
"Equals(LengthOf(Line(S, T)), y-4)",
"Equals(LengthOf(Line(R, Q)), 11)"
] | [
"RQ",
"SR",
"ST",
"TQ"
] | {"Q": [29.0, 45.0], "R": [0.0, 249.0], "S": [179.0, 199.0], "T": [203.0, 1.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, N)), 8)
- Equals(LengthOf(Line(N, Q)), 12)
- Equals(LengthOf(Line(P, Q)), 20)
- Equals(LengthOf(Line(J, H)), 4x+7)
- Equals(LengthOf(Line(J, K)), 25)
- Equals(LengthOf(Line(K, H)), 6x-2)
- Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)))
- Equals(MeasureOf(Angle... | 10 | [
"Find(LengthOf(Line(H,K)))"
] | [
"Equals(LengthOf(Line(P, N)), 8)",
"Equals(LengthOf(Line(N, Q)), 12)",
"Equals(LengthOf(Line(P, Q)), 20)",
"Equals(LengthOf(Line(J, H)), 4x+7)",
"Equals(LengthOf(Line(J, K)), 25)",
"Equals(LengthOf(Line(K, H)), 6x-2)",
"Equals(MeasureOf(Angle(H, J, K)), MeasureOf(Angle(P, Q, N)))",
"Equals(MeasureOf(A... | [
"JH",
"JK",
"KH",
"NQ",
"PN",
"PQ"
] | {"H": [2.0, 271.0], "J": [100.0, 0.0], "K": [253.0, 272.0], "N": [400.0, 80.0], "P": [253.0, 80.0], "Q": [330.0, 220.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(T, R)), x+21)
- Equals(MeasureOf(Angle(T, R, S)), 4y-10)
- Equals(MeasureOf(Angle(Z, X, Y)), 3y+5)
- Equals(LengthOf(Line(Z, X)), 2x-14)
$\triangle RST \cong \triangle XYZ$. Find $y$. | 15 | [
"Congruent(Triangle(R,S,T),Triangle(X,Y,Z))",
"Find(y)"
] | [
"Equals(LengthOf(Line(T, R)), x+21)",
"Equals(MeasureOf(Angle(T, R, S)), 4y-10)",
"Equals(MeasureOf(Angle(Z, X, Y)), 3y+5)",
"Equals(LengthOf(Line(Z, X)), 2x-14)"
] | [
"SR",
"ST",
"TR",
"XY",
"XZ",
"ZY"
] | {"R": [2.0, 56.0], "S": [55.0, 223.0], "T": [321.0, 3.0], "X": [600.0, 120.0], "Y": [550.0, -30.0], "Z": [321.0, 180.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 8)
- Equals(MeasureOf(Angle(C, B, A)), 140)
- Equals(LengthOf(Line(A, B)), 18)
- Equals(LengthOf(Line(C, A)), x)
Find x. Round to the nearest tenth. | 24.7 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), 8)",
"Equals(MeasureOf(Angle(C, B, A)), 140)",
"Equals(LengthOf(Line(A, B)), 18)",
"Equals(LengthOf(Line(C, A)), x)"
] | [
"CA",
"CB",
"AB"
] | {"C": [292.29583785278294, 84.80365384206385], "A": [0.0, 141.0], "B": [180.78661274400534, 0.7568915920984267]} | [] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(X, D))
- PointLiesOnLine(D, Line(X, T))
- PointLiesOnLine(Q, Line(X, T))
- PointLiesOnLine(D, Line(T, Q))
- PointLiesOnCircle(A, Circle(D, radius_2_0))
- PointLiesOnCircle(E, Circle(D, radius_2_0))
- PointLiesOnCircle(T, Circle(D, radius_2_0))
- PointLiesOnCircle(Q, Circle(... | 25 | [
"Equals(LengthOf(Line(E,X)),24)",
"Equals(LengthOf(Line(D,E)),7)",
"Find(LengthOf(Line(D,X)))"
] | [
"PointLiesOnLine(Q, Line(X, D))",
"PointLiesOnLine(D, Line(X, T))",
"PointLiesOnLine(Q, Line(X, T))",
"PointLiesOnLine(D, Line(T, Q))",
"PointLiesOnCircle(A, Circle(D, radius_2_0))",
"PointLiesOnCircle(E, Circle(D, radius_2_0))",
"PointLiesOnCircle(T, Circle(D, radius_2_0))",
"PointLiesOnCircle(Q, Cir... | [
"AD",
"DE",
"DQ",
"DT",
"TQ",
"XA",
"XD",
"XE",
"XQ",
"XT"
] | {"A": [336.0, 4.0], "D": [346.0, 57.0], "E": [330.0, 114.0], "Q": [290.0, 59.0], "T": [402.0, 60.0], "X": [2.0, 57.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, P, T)), 60)
- Equals(LengthOf(Line(P, T)), 4)
- Equals(LengthOf(Line(R, P)), 4)
Find $TR$. | 4 | [
"Find(LengthOf(Line(T,R)))"
] | [
"Equals(MeasureOf(Angle(R, P, T)), 60)",
"Equals(LengthOf(Line(P, T)), 4)",
"Equals(LengthOf(Line(R, P)), 4)"
] | [
"RP",
"RT",
"PT"
] | {"R": [273.7379557680813, 259.62363020522014], "P": [178.43508290041999, 1.2755717441929733], "T": [0.0, 214.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(X, W)), 4)
- Equals(MeasureOf(Angle(X, Y, W)), 23)
- Equals(LengthOf(Line(W, Z)), 4)
- Perpendicular(Line(Y, X), Line(X, W))
- Perpendicular(Line(W, Z), Line(Y, Z))
Find z | 2 \sqrt { 6 } | [
"Find(z)"
] | [
"Equals(LengthOf(Line(X, W)), 4)",
"Equals(MeasureOf(Angle(X, Y, W)), 23)",
"Equals(LengthOf(Line(W, Z)), 4)",
"Perpendicular(Line(Y, X), Line(X, W))",
"Perpendicular(Line(W, Z), Line(Y, Z))"
] | [
"WZ",
"XW",
"YE",
"YF",
"YG",
"YW",
"YX"
] | {"Z": [86.0, 230.0], "W": [47.0, 132.0], "X": [86.0, 30.0], "Y": [343.0, 133.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 7))
- Equals(MeasureOf(Angle(D, F, B)), 63)
- Equals(MeasureOf(Angle(F, D, E)), 69)
- Equals(MeasureOf(Angle(F, B, D)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(B, D, F)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, D, G)), 47)
- Equals(Mea... | 32 | [
"Equals(MeasureOf(Angle(4)),MeasureOf(Angle(5)))",
"Find(MeasureOf(Angle(4)))"
] | [
"Equals(MeasureOf(Angle(C, E, D)), MeasureOf(angle 7))",
"Equals(MeasureOf(Angle(D, F, B)), 63)",
"Equals(MeasureOf(Angle(F, D, E)), 69)",
"Equals(MeasureOf(Angle(F, B, D)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(B, D, F)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, D, G)), 47)",
"Equals(Me... | [
"AB",
"AD",
"AF",
"BC",
"BD",
"BF",
"BG",
"CE",
"CG",
"DC",
"DE",
"DF",
"DG"
] | {"A": [226.0, 268.0], "B": [0.0, 139.0], "C": [438.0, 139.0], "D": [161.0, 139.0], "E": [292.0, 1.0], "F": [96.0, 8.0], "G": [570.0, 139.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 5)
- Equals(LengthOf(Line(O, B)), 21.5)
- Equals(LengthOf(Line(O, C)), 8)
- Equals(LengthOf(Line(A, C)), 15)
- PointLiesOnLine(A, Line(C, B))
- Perpendicular(Line(O, C), Line(C, A))
Find the perimeter of the triangle. Round to the nearest tenth if necessary. | 43.5 | [
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(A, B)), 5)",
"Equals(LengthOf(Line(O, B)), 21.5)",
"Equals(LengthOf(Line(O, C)), 8)",
"Equals(LengthOf(Line(A, C)), 15)",
"PointLiesOnLine(A, Line(C, B))",
"Perpendicular(Line(O, C), Line(C, A))"
] | [
"AB",
"AC",
"AO",
"BC",
"OB",
"OC"
] | {"A": [227.0, 121.0], "B": [300.0, 121.0], "C": [2.0, 120.0], "O": [2.0, 2.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(R, Line(Z, Y))
- PointLiesOnLine(Q, Line(Z, X))
If $\overline{QR} \| \overline{XY}, XQ=15, QZ=12$, and $YR=20$, what is the length of $\overline{RZ}$. | 16 | [
"Parallel(Line(Q,R),Line(X,Y))",
"Equals(LengthOf(Line(X,Q)),15)",
"Equals(LengthOf(Line(Q,Z)),12)",
"Equals(LengthOf(Line(Y,R)),20)",
"Find(LengthOf(Line(R,Z)))"
] | [
"PointLiesOnLine(R, Line(Z, Y))",
"PointLiesOnLine(Q, Line(Z, X))"
] | [
"QX",
"QZ",
"RQ",
"RY",
"RZ",
"YX",
"ZX",
"ZY"
] | {"Q": [21.0, 128.0], "R": [215.0, 158.0], "X": [2.0, 2.0], "Y": [364.0, 61.0], "Z": [42.0, 269.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), y)
- Equals(MeasureOf(Angle(B, A, C)), 60)
- Equals(LengthOf(Line(A, C)), 8)
- Equals(LengthOf(Line(B, C)), x)
- Perpendicular(Line(A, C), Line(B, C))
Find $x$. | 13.9 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), y)",
"Equals(MeasureOf(Angle(B, A, C)), 60)",
"Equals(LengthOf(Line(A, C)), 8)",
"Equals(LengthOf(Line(B, C)), x)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.0, 1.0], "B": [251.0, 9.0], "C": [71.0, 116.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(R, P, S)), 130)
- Equals(MeasureOf(Angle(T, P, Q)), 112)
- PointLiesOnLine(P, Line(T, R))
- PointLiesOnCircle(S, Circle(P, radius_5_0))
- PointLiesOnCircle(T, Circle(P, radius_5_0))
- PointLiesOnCircle(R, Circle(P, radius_5_0))
- PointLiesOnCircle(Q, Circle(P, radius_5_0))
... | 4.75 | [
"Circle(P)",
"Equals(LengthOf(Line(P,S)),4)",
"Find(LengthOf(Arc(Q,R)))"
] | [
"Equals(MeasureOf(Angle(R, P, S)), 130)",
"Equals(MeasureOf(Angle(T, P, Q)), 112)",
"PointLiesOnLine(P, Line(T, R))",
"PointLiesOnCircle(S, Circle(P, radius_5_0))",
"PointLiesOnCircle(T, Circle(P, radius_5_0))",
"PointLiesOnCircle(R, Circle(P, radius_5_0))",
"PointLiesOnCircle(Q, Circle(P, radius_5_0))"... | [
"PQ",
"PR",
"PT",
"SP",
"TR"
] | {"P": [152.0, 155.0], "Q": [1.0, 132.0], "R": [119.0, 4.0], "S": [288.0, 222.0], "T": [188.0, 301.0]} | [
"P"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(L, J, M)), MeasureOf(Angle(T, Q, S)))
- Equals(MeasureOf(Angle(J, M, L)), MeasureOf(Angle(S, T, Q)))
- Equals(LengthOf(Line(M, J)), 4)
- Equals(LengthOf(Line(S, T)), 3)
- Equals(LengthOf(Line(T, Q)), 2)
- Equals(LengthOf(Line(S, Q)), 5)
- Equals(LengthOf(Line(M, L)), 6x-3)
-... | 4 | [
"Similar(Triangle(J,L,M),Triangle(Q,S,T))",
"Find(y)"
] | [
"Equals(MeasureOf(Angle(L, J, M)), MeasureOf(Angle(T, Q, S)))",
"Equals(MeasureOf(Angle(J, M, L)), MeasureOf(Angle(S, T, Q)))",
"Equals(LengthOf(Line(M, J)), 4)",
"Equals(LengthOf(Line(S, T)), 3)",
"Equals(LengthOf(Line(T, Q)), 2)",
"Equals(LengthOf(Line(S, Q)), 5)",
"Equals(LengthOf(Line(M, L)), 6x-3)"... | [
"JL",
"JM",
"ML",
"SQ",
"ST",
"TQ"
] | {"J": [0.0, 1.0], "L": [1.0, 279.0], "M": [274.0, 83.0], "Q": [450.0, 200.0], "S": [470.0, 1.0], "T": [320.0, 120.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(M, Q)), 5)
- Equals(LengthOf(Line(O, N)), 3+\frac{3}{5})
- Equals(LengthOf(Line(M, N)), 6)
- PointLiesOnLine(N, Line(O, M))
- PointLiesOnLine(Q, Line(M, P))
- Parallel(Line(N, Q), Line(O, P))
Find $MP$. | 8 | [
"Find(LengthOf(Line(M,P)))"
] | [
"Equals(LengthOf(Line(M, Q)), 5)",
"Equals(LengthOf(Line(O, N)), 3+\\frac{3}{5})",
"Equals(LengthOf(Line(M, N)), 6)",
"PointLiesOnLine(N, Line(O, M))",
"PointLiesOnLine(Q, Line(M, P))",
"Parallel(Line(N, Q), Line(O, P))"
] | [
"MN",
"MP",
"MQ",
"NQ",
"OM",
"ON",
"OP",
"PQ"
] | {"M": [123.0, 4.0], "N": [258.0, 217.0], "O": [303.0, 293.0], "P": [2.0, 308.0], "Q": [33.0, 227.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(C, D)), y)
- Equals(LengthOf(Line(A, D)), z)
- Equals(LengthOf(Line(B, C)), 12)
- Equals(LengthOf(Line(B, D)), 4)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(C, D), Line(B, D))
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 24 \sqrt { 2 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(C, D)), y)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(B, C)), 12)",
"Equals(LengthOf(Line(B, D)), 4)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(C, D), Line(B, D))",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [256.0, 1.0], "B": [1.0, 0.0], "C": [256.0, 234.0], "D": [140.0, 128.0]} | [
""
] |
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 $x$. | 10.4 | [
"Similar(Shape($1),Shape($2))",
"Find(x)"
] | [
"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(X, Y)), 4)
- PointLiesOnCircle(Z, Circle(X, radius_0_0))
- PointLiesOnCircle(Y, Circle(X, radius_0_0))
- Equals(MeasureOf(Angle(X, Y)), 4)
-
Find the length of $\widehat {ZY}$. Round to the nearest hundredth. | 5.24 | [
"Find(LengthOf(Arc(Z,Y)))"
] | [
"Equals(LengthOf(Line(X, Y)), 4)",
"PointLiesOnCircle(Z, Circle(X, radius_0_0))",
"PointLiesOnCircle(Y, Circle(X, radius_0_0))",
"Equals(MeasureOf(Angle(X, Y)), 4)",
""
] | [
"XY",
"XZ"
] | {"X": [128.0, 128.0], "Y": [97.0, 5.0], "Z": [2.0, 127.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(E, B, A)), 30)
- Equals(MeasureOf(Angle(D, B, E)), x)
- Equals(MeasureOf(Angle(C, B, D)), 110)
- PointLiesOnCircle(A, Circle(B, radius_1_0))
- PointLiesOnCircle(C, Circle(B, radius_1_0))
- PointLiesOnCircle(D, Circle(B, radius_1_0))
- PointLiesOnCircle(E, Circle(B, radius_1_... | 130 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(E, B, A)), 30)",
"Equals(MeasureOf(Angle(D, B, E)), x)",
"Equals(MeasureOf(Angle(C, B, D)), 110)",
"PointLiesOnCircle(A, Circle(B, radius_1_0))",
"PointLiesOnCircle(C, Circle(B, radius_1_0))",
"PointLiesOnCircle(D, Circle(B, radius_1_0))",
"PointLiesOnCircle(E, Circle(B, radius_1... | [
"AB",
"AE",
"BC",
"BD",
"BE"
] | {"A": [168.30712454533213, 12.385750909335755], "B": [117.40138436884067, 115.47190744524228], "C": [222.99371704358114, 166.5060065486671], "D": [33.536117346541275, 197.47042066987996], "E": [105.18081665559488, 1.470642132171676]} | [
"B"
] |
Diagram Logic Form:
- Equals(MeasureOf(Arc(A,B)),102)
- PointLiesOnLine(C, Line(B, F))
- PointLiesOnLine(A, Line(B, H))
- PointLiesOnCircle(B, Circle(G, radius_3_0))
- PointLiesOnCircle(A, Circle(G, radius_3_0))
Find $m \angle A B C$ if $m \widehat{A B}=102$ | 129 | [
"Equals(MeasureOf(Arc(A,B)),102)",
"Find(MeasureOf(Angle(A,B,C)))"
] | [
"Equals(MeasureOf(Arc(A,B)),102)",
"PointLiesOnLine(C, Line(B, F))",
"PointLiesOnLine(A, Line(B, H))",
"PointLiesOnCircle(B, Circle(G, radius_3_0))",
"PointLiesOnCircle(A, Circle(G, radius_3_0))"
] | [
"BA",
"BC",
"BF",
"BH",
"FC",
"HA"
] | {"A": [40.0, 95.0], "B": [153.0, 181.0], "C": [219.0, 167.0], "F": [258.0, 160.0], "G": [132.0, 93.0], "H": [0.0, 64.0]} | [
"G"
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(P, S))
- PointLiesOnLine(R, Line(Q, S))
- Parallel(Line(P, Q), Line(T, R))
If $R T=15, Q P=21,$ and $P T=8,$ find $T S$ | 20 | [
"Equals(LengthOf(Line(R,T)),15)",
"Equals(LengthOf(Line(Q,P)),21)",
"Equals(LengthOf(Line(P,T)),8)",
"Find(LengthOf(Line(T,S)))"
] | [
"PointLiesOnLine(T, Line(P, S))",
"PointLiesOnLine(R, Line(Q, S))",
"Parallel(Line(P, Q), Line(T, R))"
] | [
"PQ",
"PS",
"PT",
"QR",
"QS",
"RS",
"TS"
] | {"P": [0.0, 148.0], "Q": [49.0, 8.0], "R": [96.0, 46.0], "S": [209.0, 149.0], "T": [59.0, 148.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(K, L, N)), 18)
- Equals(MeasureOf(Angle(J, L, K)), 25)
- Equals(MeasureOf(Angle(N, L, M)), 20)
- Equals(LengthOf(Line(K, L)), LengthOf(Line(N, L)))
- Equals(LengthOf(Line(N, M)), LengthOf(Line(M, L)))
$\triangle K L N$ and $\triangle L M N$ are isosceles and $m \angle J K N... | 81 | [
"Isosceles(Triangle(K,L,N))",
"Isosceles(Triangle(L,M,N))",
"Equals(MeasureOf(Angle(J,K,N)),130)",
"Find(MeasureOf(Angle(L,K,N)))"
] | [
"Equals(MeasureOf(Angle(K, L, N)), 18)",
"Equals(MeasureOf(Angle(J, L, K)), 25)",
"Equals(MeasureOf(Angle(N, L, M)), 20)",
"Equals(LengthOf(Line(K, L)), LengthOf(Line(N, L)))",
"Equals(LengthOf(Line(N, M)), LengthOf(Line(M, L)))"
] | [
"JK",
"KL",
"KN",
"LJ",
"ML",
"NL",
"NM"
] | {"J": [5.0, 94.0], "K": [69.0, 3.0], "L": [55.0, 219.0], "M": [133.0, 134.0], "N": [138.0, 18.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(B, C, A)), 87)
- Equals(LengthOf(Line(A, C)), 21)
- Equals(MeasureOf(Angle(A, B, C)), 37)
- Equals(LengthOf(Line(A, B)), x)
Find x. Round the side measure to the nearest tenth. | 34.8 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(B, C, A)), 87)",
"Equals(LengthOf(Line(A, C)), 21)",
"Equals(MeasureOf(Angle(A, B, C)), 37)",
"Equals(LengthOf(Line(A, B)), x)"
] | [
"AB",
"AC",
"BC"
] | {"A": [0.6624724919093978, 164.00636893203884], "B": [318.70485866229535, 162.00280197472503], "C": [108.0, 0.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 5\sqrt{26})
- Equals(MeasureOf(Angle(D, C, A)), x)
- Equals(LengthOf(Line(C, D)), 5)
- Equals(LengthOf(Line(C, B)), \sqrt{26})
- Equals(LengthOf(Line(A, D)), 25)
- Equals(LengthOf(Line(D, B)), 1)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(A, C), Line(C, B))
... | \sqrt { 26 } / 26 | [
"Find(SinOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(A, C)), 5\\sqrt{26})",
"Equals(MeasureOf(Angle(D, C, A)), x)",
"Equals(LengthOf(Line(C, D)), 5)",
"Equals(LengthOf(Line(C, B)), \\sqrt{26})",
"Equals(LengthOf(Line(A, D)), 25)",
"Equals(LengthOf(Line(D, B)), 1)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(A, C), Line(C... | [
"AC",
"BC",
"CD",
"AD",
"AB",
"BD"
] | {"A": [0.0, 132.0], "B": [683.0, 135.0], "D": [652.0, 135.0], "C": [649.0, 1.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(M, Line(X, Y))
- PointLiesOnLine(N, Line(X, Z))
- Parallel(Line(M, N), Line(Y, Z))
If XM = 4, XN = 6, and NZ = 9, find XY. | 10 | [
"Equals(LengthOf(Line(X,M)),4)",
"Equals(LengthOf(Line(X,N)),6)",
"Equals(LengthOf(Line(N,Z)),9)",
"Find(LengthOf(Line(X,Y)))"
] | [
"PointLiesOnLine(M, Line(X, Y))",
"PointLiesOnLine(N, Line(X, Z))",
"Parallel(Line(M, N), Line(Y, Z))"
] | [
"MN",
"XM",
"XY",
"YM",
"ZX",
"ZY",
"NX",
"NZ"
] | {"M": [63.0, 81.0], "N": [78.0, 126.0], "X": [2.0, 127.0], "Y": [167.0, 1.0], "Z": [210.0, 126.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(X, B)), x+16)
- Equals(LengthOf(Line(A, C)), 16)
- Equals(LengthOf(Line(X, C)), x)
- PointLiesOnLine(X, Line(C, B))
- PointLiesOnCircle(A, Circle(D, radius_3_0))
- PointLiesOnCircle(B, Circle(D, radius_3_0))
- PointLiesOnCircle(X, Circle(D, radius_3_0))
Find x. Round to the n... | 8 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(X, B)), x+16)",
"Equals(LengthOf(Line(A, C)), 16)",
"Equals(LengthOf(Line(X, C)), x)",
"PointLiesOnLine(X, Line(C, B))",
"PointLiesOnCircle(A, Circle(D, radius_3_0))",
"PointLiesOnCircle(B, Circle(D, radius_3_0))",
"PointLiesOnCircle(X, Circle(D, radius_3_0))"
] | [
"AC",
"AX",
"CB",
"CX",
"XB"
] | {"A": [157.0, 143.0], "B": [7.0, 117.0], "C": [253.0, 93.0], "D": [88.0, 86.0], "X": [171.0, 100.0]} | [
"D"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 43)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(A, D)), 4)
- Equals(LengthOf(Line(B, D)), 6)
- PointLiesOnLine(D, Line(A, B))
- Equals(MeasureOf(Angle(A, C, D)), MeasureOf(Angle(D, C, B)))
Find $x$. | \frac { 26 } { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(B, C)), 43)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, D)), 4)",
"Equals(LengthOf(Line(B, D)), 6)",
"PointLiesOnLine(D, Line(A, B))",
"Equals(MeasureOf(Angle(A, C, D)), MeasureOf(Angle(D, C, B)))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 203.0], "B": [373.0, 204.0], "C": [103.0, 0.0], "D": [154.0, 204.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(M, J, B)), MeasureOf(angle 1))
- Equals(MeasureOf(Angle(E, P, C)), MeasureOf(angle 2))
- Equals(MeasureOf(Angle(A, G, K)), MeasureOf(angle 3))
- Equals(MeasureOf(Angle(P, O, R)), MeasureOf(angle 4))
- Equals(MeasureOf(Angle(P, R, O)), MeasureOf(angle 5))
- Equals(MeasureOf(A... | 110 | [
"Equals(MeasureOf(Angle(1)),50)",
"Equals(MeasureOf(Angle(3)),60)",
"Find(MeasureOf(Angle(2)))"
] | [
"Equals(MeasureOf(Angle(M, J, B)), MeasureOf(angle 1))",
"Equals(MeasureOf(Angle(E, P, C)), MeasureOf(angle 2))",
"Equals(MeasureOf(Angle(A, G, K)), MeasureOf(angle 3))",
"Equals(MeasureOf(Angle(P, O, R)), MeasureOf(angle 4))",
"Equals(MeasureOf(Angle(P, R, O)), MeasureOf(angle 5))",
"Equals(MeasureOf(Ang... | [
"AB",
"AF",
"AG",
"AH",
"AJ",
"AN",
"AQ",
"AR",
"AS",
"AT",
"AU",
"BF",
"BG",
"BJ",
"BT",
"CI",
"CK",
"CM",
"CP",
"DO",
"DW",
"EL",
"FE",
"FG",
"FJ",
"FL",
"FN",
"FO",
"FP",
"FS",
"FT",
"GC",
"GI",
"GJ",
"GK",
"GP",
"GQ",
"GR",
"GT",
"HC"... | {"A": [324.0, 147.0], "B": [0.0, 146.0], "C": [183.0, 39.0], "D": [490.0, 123.0], "E": [66.0, 226.0], "F": [135.0, 146.0], "G": [279.0, 147.0], "H": [211.0, 7.0], "I": [151.0, 2.0], "J": [89.0, 146.0], "K": [347.0, 224.0], "L": [262.0, 1.0], "M": [20.0, 226.0], "N": [229.0, 39.0], "O": [156.0, 123.0], "P": [206.0, 65.0... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 6)
- Equals(LengthOf(Line(C, A)), 20)
- Perpendicular(Line(C, B), Line(C, A))
Find the measure of $∠A$ to the nearest tenth. | 16.7 | [
"Find(MeasureOf(Angle(A)))"
] | [
"Equals(LengthOf(Line(C, B)), 6)",
"Equals(LengthOf(Line(C, A)), 20)",
"Perpendicular(Line(C, B), Line(C, A))"
] | [
"CA",
"CB",
"AB"
] | {"C": [0.022724892658914086, 131.00010472300764], "A": [434.0, 132.0], "B": [2.000658761528342, 0.6376811594202962]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, D)), 4)
- Equals(LengthOf(Line(B, D)), 9)
- Equals(LengthOf(Line(A, C)), x)
- Equals(LengthOf(Line(A, D)), z)
- Equals(LengthOf(Line(A, B)), y)
- PointLiesOnLine(D, Line(B, C))
- Perpendicular(Line(B, D), Line(A, D))
- Perpendicular(Line(A, C), Line(A, B))
Find x. | 2 \sqrt { 13 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, D)), 4)",
"Equals(LengthOf(Line(B, D)), 9)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(LengthOf(Line(A, D)), z)",
"Equals(LengthOf(Line(A, B)), y)",
"PointLiesOnLine(D, Line(B, C))",
"Perpendicular(Line(B, D), Line(A, D))",
"Perpendicular(Line(A, C), Line(A, B))"
] | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [2.0, 139.0], "B": [287.0, 140.0], "C": [1.0, 1.0], "D": [57.0, 28.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, E, U)), 8x+4)
- Equals(MeasureOf(Angle(F, T, V)), 9x-11)
- Equals(LengthOf(Line(A, D)), 5)
- PointLiesOnLine(T, Line(R, B))
- PointLiesOnLine(E, Line(R, B))
- PointLiesOnLine(E, Line(R, T))
- PointLiesOnLine(T, Line(B, E))
- PointLiesOnLine(R, Line(B, F))
- PointLiesOnLin... | 124 | [
"Parallel(Line(m),Line(n))",
"Find(MeasureOf(Angle(R,S,U)))"
] | [
"Equals(MeasureOf(Angle(F, E, U)), 8x+4)",
"Equals(MeasureOf(Angle(F, T, V)), 9x-11)",
"Equals(LengthOf(Line(A, D)), 5)",
"PointLiesOnLine(T, Line(R, B))",
"PointLiesOnLine(E, Line(R, B))",
"PointLiesOnLine(E, Line(R, T))",
"PointLiesOnLine(T, Line(B, E))",
"PointLiesOnLine(R, Line(B, F))",
"PointLi... | [
"AD",
"AU",
"BE",
"BF",
"BT",
"CV",
"DU",
"EA",
"ED",
"EF",
"EU",
"RB",
"RE",
"RF",
"RT",
"TC",
"TE",
"TF",
"TV"
] | {"A": [301.0, 1.0], "B": [443.0, 196.0], "C": [154.0, 201.0], "D": [0.0, 151.0], "E": [155.0, 74.0], "F": [1.0, 6.0], "R": [44.0, 27.0], "T": [292.0, 132.0], "U": [253.0, 22.0], "V": [444.0, 57.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), 5\sqrt{26})
- Equals(MeasureOf(Angle(D, C, A)), x)
- Equals(LengthOf(Line(C, D)), 5)
- Equals(LengthOf(Line(C, B)), \sqrt{26})
- Equals(LengthOf(Line(A, D)), 25)
- Equals(LengthOf(Line(D, B)), 1)
- PointLiesOnLine(D, Line(A, B))
- Perpendicular(Line(A, C), Line(C, B))
... | 5 | [
"Find(TanOf(Angle(B)))"
] | [
"Equals(LengthOf(Line(A, C)), 5\\sqrt{26})",
"Equals(MeasureOf(Angle(D, C, A)), x)",
"Equals(LengthOf(Line(C, D)), 5)",
"Equals(LengthOf(Line(C, B)), \\sqrt{26})",
"Equals(LengthOf(Line(A, D)), 25)",
"Equals(LengthOf(Line(D, B)), 1)",
"PointLiesOnLine(D, Line(A, B))",
"Perpendicular(Line(A, C), Line(C... | [
"AB",
"AC",
"AD",
"BC",
"BD",
"CD"
] | {"A": [0.0, 132.0], "B": [683.0, 135.0], "C": [649.0, 1.0], "D": [652.0, 135.0]} | [
""
] |
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... | 7 | [
"Equals(LengthOf(Line(R,P)),3.5)",
"Equals(LengthOf(Line(J,P)),9)",
"Find(LengthOf(Line(P,L)))"
] | [
"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(... | [
"JC",
"JK",
"JL",
"JR",
"JS",
"JT",
"KR",
"KS",
"KT",
"LC",
"LK",
"LR",
"LS",
"LT",
"PJ",
"PK",
"PL",
"PR",
"PS",
"PT",
"TC"
] | {"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], "S": [365.0, 33.0], "T": [271.0, 218.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(S, Line(W, Y))
- PointLiesOnLine(S, Line(Q, P))
- PointLiesOnLine(Q, Line(W, X))
- PointLiesOnLine(B, Line(Y, X))
- PointLiesOnLine(B, Line(Q, R))
- PointLiesOnLine(B, Line(Q, R))
- PointLiesOnLine(Y, Line(P, R))
- Perpendicular(Line(C, P), Line(Y, S))
- Perpendicular(Line(Y, S), L... | 4 | [
"Parallel(Line(P,R),Line(W,X))",
"Equals(LengthOf(Line(W,X)),10)",
"Equals(LengthOf(Line(X,Y)),6)",
"Equals(LengthOf(Line(W,Y)),8)",
"Equals(LengthOf(Line(R,Y)),5)",
"Equals(LengthOf(Line(P,S)),3)",
"Find(LengthOf(Line(S,Y)))"
] | [
"PointLiesOnLine(S, Line(W, Y))",
"PointLiesOnLine(S, Line(Q, P))",
"PointLiesOnLine(Q, Line(W, X))",
"PointLiesOnLine(B, Line(Y, X))",
"PointLiesOnLine(B, Line(Q, R))",
"PointLiesOnLine(B, Line(Q, R))",
"PointLiesOnLine(Y, Line(P, R))",
"Perpendicular(Line(C, P), Line(Y, S))",
"Perpendicular(Line(Y... | [
"PR",
"QB",
"QP",
"QR",
"QS",
"QX",
"RB",
"SP",
"WQ",
"WS",
"WX",
"WY",
"XB",
"YB",
"YP",
"YR",
"YS",
"YX"
] | {"B": [120.0, 130.0], "P": [290.0, 0.0], "Q": [291.0, 133.0], "R": [3.0, 131.0], "S": [291.0, 82.0], "W": [409.0, 81.0], "X": [121.0, 212.0], "Y": [119.0, 80.0]} | [
""
] |
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... | 2 \sqrt { 5 } | [
"Find(x)"
] | [
"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(LengthOf(Line(K, A)), 4x)
- Equals(LengthOf(Line(C, G)), 2x)
- Equals(LengthOf(Line(H, A)), x)
- Equals(LengthOf(Line(H, C)), x)
- PointLiesOnLine(C, Line(J, H))
- PointLiesOnLine(B, Line(J, K))
- PointLiesOnLine(A, Line(K, H))
- PointLiesOnCircle(B, Circle(J, radius_0_0))
- PointLiesOnCirc... | 24 | [
"Equals(SumOf(CircumferenceOf(Circle(H)),Circle(J),Circle(K)),56\\pi)",
"Find(LengthOf(Line(K,J)))"
] | [
"Equals(LengthOf(Line(K, A)), 4x)",
"Equals(LengthOf(Line(C, G)), 2x)",
"Equals(LengthOf(Line(H, A)), x)",
"Equals(LengthOf(Line(H, C)), x)",
"PointLiesOnLine(C, Line(J, H))",
"PointLiesOnLine(B, Line(J, K))",
"PointLiesOnLine(A, Line(K, H))",
"PointLiesOnCircle(B, Circle(J, radius_0_0))",
"PointLie... | [
"HA",
"HC",
"JB",
"JC",
"JH",
"JK",
"KA",
"KB",
"KH"
] | {"A": [380.0, 160.0], "B": [359.0, 281.0], "C": [452.0, 213.0], "H": [445.0, 150.0], "J": [465.0, 334.0], "K": [196.0, 191.0]} | [
"J",
"K",
"H"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(H, E, G)), 6x+2)
- Equals(MeasureOf(Angle(H, F, G)), 3x+23)
- PointLiesOnLine(I, Line(H, F))
- PointLiesOnLine(I, Line(E, G))
- PointLiesOnCircle(E, Circle(B, radius_4_0))
- PointLiesOnCircle(G, Circle(B, radius_4_0))
- PointLiesOnCircle(H, Circle(B, radius_4_0))
- PointLies... | 7 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(H, E, G)), 6x+2)",
"Equals(MeasureOf(Angle(H, F, G)), 3x+23)",
"PointLiesOnLine(I, Line(H, F))",
"PointLiesOnLine(I, Line(E, G))",
"PointLiesOnCircle(E, Circle(B, radius_4_0))",
"PointLiesOnCircle(G, Circle(B, radius_4_0))",
"PointLiesOnCircle(H, Circle(B, radius_4_0))",
"Point... | [
"HE",
"HF",
"GE",
"GF",
"EI",
"IG",
"HI",
"IF"
] | {"E": [115.0, 1.0], "F": [221.0, 65.0], "G": [179.0, 219.0], "H": [12.0, 167.0], "I": [144.0, 102.0]} | [
"B"
] |
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(2)))"
] | [
"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... | [
"CG",
"CA",
"CB",
"GD",
"GA",
"GF",
"GB",
"AD",
"AF",
"AB",
"DF"
] | {"C": [467.3028007071389, 179.32857098008682], "G": [245.71043804039223, 179.38710896331065], "D": [0.0, 1.0], "A": [464.76705978377527, 1.2643739086495174], "F": [244.00841171251108, 0.761259982253776], "B": [372.8431907794965, 75.82984531392174]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, K)), 4x+3)
- Equals(LengthOf(Line(J, K)), 6x-5)
- Equals(LengthOf(Line(M, P)), 3y+8)
- Equals(LengthOf(Line(Q, P)), 5y-7)
- Equals(LengthOf(Line(Q, P)), LengthOf(Line(M, P)))
- PointLiesOnLine(P, Line(M, Q))
- PointLiesOnLine(K, Line(J, L))
- Parallel(Line(J, M), Line(K, P)... | 4 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(L, K)), 4x+3)",
"Equals(LengthOf(Line(J, K)), 6x-5)",
"Equals(LengthOf(Line(M, P)), 3y+8)",
"Equals(LengthOf(Line(Q, P)), 5y-7)",
"Equals(LengthOf(Line(Q, P)), LengthOf(Line(M, P)))",
"PointLiesOnLine(P, Line(M, Q))",
"PointLiesOnLine(K, Line(J, L))",
"Parallel(Line(J, M), Line(K... | [
"JK",
"JL",
"KL",
"MP",
"PQ",
"MQ",
"JM",
"KP",
"LQ"
] | {"L": [538.0, 78.0], "J": [100.0, 152.0], "K": [321.0, 114.0], "M": [129.0, 254.0], "P": [364.0, 262.0], "Q": [589.0, 262.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, G, C)), 60)
- PointLiesOnLine(G, Line(E, C))
- PointLiesOnLine(G, Line(A, B))
- PointLiesOnCircle(E, Circle(G, radius_0_0))
- PointLiesOnCircle(C, Circle(G, radius_0_0))
- PointLiesOnCircle(A, Circle(G, radius_0_0))
- PointLiesOnCircle(D, Circle(G, radius_0_0))
- PointLie... | 30 | [
"Find(MeasureOf(Angle(D,G,E)))"
] | [
"Equals(MeasureOf(Angle(A, G, C)), 60)",
"PointLiesOnLine(G, Line(E, C))",
"PointLiesOnLine(G, Line(A, B))",
"PointLiesOnCircle(E, Circle(G, radius_0_0))",
"PointLiesOnCircle(C, Circle(G, radius_0_0))",
"PointLiesOnCircle(A, Circle(G, radius_0_0))",
"PointLiesOnCircle(D, Circle(G, radius_0_0))",
"Poin... | [
"AB",
"EC",
"GA",
"GB",
"GC",
"GD",
"GE"
] | {"A": [1.0, 82.0], "B": [169.0, 86.0], "C": [44.0, 12.0], "D": [85.0, 159.0], "E": [126.0, 158.0], "G": [86.0, 85.0]} | [
"G"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(P, O)), p)
- Equals(LengthOf(Line(M, N)), q)
- Equals(MeasureOf(Angle(A, B, D)), 3x-60)
- Equals(MeasureOf(Angle(D, B, C)), y)
- Equals(MeasureOf(Angle(E, C, F)), 2x+15)
- PointLiesOnLine(A, Line(B, I))
- PointLiesOnLine(A, Line(C, I))
- PointLiesOnLine(A, Line(F, I))
- PointL... | 45 | [
"Shape($)",
"Parallel(Line(p),Line(q))",
"Find(x)"
] | [
"Equals(LengthOf(Line(P, O)), p)",
"Equals(LengthOf(Line(M, N)), q)",
"Equals(MeasureOf(Angle(A, B, D)), 3x-60)",
"Equals(MeasureOf(Angle(D, B, C)), y)",
"Equals(MeasureOf(Angle(E, C, F)), 2x+15)",
"PointLiesOnLine(A, Line(B, I))",
"PointLiesOnLine(A, Line(C, I))",
"PointLiesOnLine(A, Line(F, I))",
... | [
"AF",
"BA",
"BD",
"BF",
"BG",
"BH",
"BO",
"BP",
"BQ",
"BR",
"BU",
"CA",
"CB",
"CE",
"CF",
"CI",
"CJ",
"CK",
"CL",
"CM",
"CN",
"CS",
"CT",
"CV",
"DO",
"DP",
"DQ",
"DR",
"DU",
"ES",
"ET",
"EV",
"GD",
"GH",
"GO",
"GP",
"GQ",
"GR",
"GU",
"HD"... | {"A": [195.0, 31.0], "B": [192.0, 79.0], "C": [181.0, 162.0], "D": [315.0, 57.0], "E": [335.0, 132.0], "F": [178.0, 203.0], "G": [380.0, 45.0], "H": [44.0, 108.0], "I": [202.0, 1.0], "J": [67.0, 182.0], "K": [358.0, 129.0], "L": [172.0, 236.0], "M": [425.0, 116.0], "N": [25.0, 191.0], "O": [1.0, 116.0], "P": [403.0, 39... | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(Y, X)), 4x+5)
- Equals(LengthOf(Line(W, Y)), 6x+3)
- Equals(LengthOf(Line(W, X)), 9x)
- Equals(LengthOf(Line(X, x)), LengthOf(Line(W, Y)))
- Equals(LengthOf(Line(W, Y)), LengthOf(Line(Y, X)))
Find the length of $WY$ | 9 | [
"Find(LengthOf(Line(W,Y)))"
] | [
"Equals(LengthOf(Line(Y, X)), 4x+5)",
"Equals(LengthOf(Line(W, Y)), 6x+3)",
"Equals(LengthOf(Line(W, X)), 9x)",
"Equals(LengthOf(Line(X, x)), LengthOf(Line(W, Y)))",
"Equals(LengthOf(Line(W, Y)), LengthOf(Line(Y, X)))"
] | [
"WX",
"WY",
"YX"
] | {"W": [0.0, 155.0], "X": [92.0, 1.0], "Y": [180.0, 156.0]} | [
""
] |
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 $m\angle U$ | 134 | [
"Find(MeasureOf(Angle(W)))"
] | [
"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)"
] | [
"WV",
"WT",
"VU",
"TU"
] | {"W": [245.66261808367074, 112.33738191632929], "U": [110.00892057464263, 1.9999283487980506], "V": [356.9946018893387, 0.6720647773279325], "T": [0.0, 113.0]} | [] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(F, D, H)), 28)
- PointLiesOnLine(G, Line(D, H))
- Equals(LengthOf(Line(F, G)), LengthOf(Line(H, F)))
- Equals(LengthOf(Line(H, A)), LengthOf(Line(D, G)))
$\Delta DFG$ and $\Delta F G H$ are isosceles, $m \angle FDH=28$ and$\overline{DG} \cong \overline{FG} \cong \overline{... | 68 | [
"Isosceles(Triangle(D,F,G))",
"Isosceles(Triangle(F,G,H))",
"Equals(MeasureOf(Angle(F,D,H)),28)",
"Equals(LengthOf(Line(D,G)),Line(F,G))",
"Equals(LengthOf(Line(F,G)),Line(F,H))",
"Find(MeasureOf(Angle(G,F,H)))"
] | [
"Equals(MeasureOf(Angle(F, D, H)), 28)",
"PointLiesOnLine(G, Line(D, H))",
"Equals(LengthOf(Line(F, G)), LengthOf(Line(H, F)))",
"Equals(LengthOf(Line(H, A)), LengthOf(Line(D, G)))"
] | [
"DG",
"DH",
"FD",
"FG",
"FH",
"HG"
] | {"D": [1.0, 105.0], "F": [193.0, 2.0], "G": [160.0, 106.0], "H": [227.0, 106.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(I, J)), \frac{4}{2}y+1)
- Equals(LengthOf(Line(H, A)), 6-x)
- Equals(LengthOf(Line(E, N)), 2y)
- Equals(LengthOf(Line(B, H)), 2x+3)
- PointLiesOnLine(H, Line(A, B))
- PointLiesOnLine(B, Line(A, G))
- PointLiesOnLine(H, Line(A, G))
- PointLiesOnLine(E, Line(A, N))
- PointLiesOn... | 1.5 | [
"Find(y)"
] | [
"Equals(LengthOf(Line(I, J)), \\frac{4}{2}y+1)",
"Equals(LengthOf(Line(H, A)), 6-x)",
"Equals(LengthOf(Line(E, N)), 2y)",
"Equals(LengthOf(Line(B, H)), 2x+3)",
"PointLiesOnLine(H, Line(A, B))",
"PointLiesOnLine(B, Line(A, G))",
"PointLiesOnLine(H, Line(A, G))",
"PointLiesOnLine(E, Line(A, N))",
"Poi... | [
"AB",
"AE",
"AG",
"AH",
"AK",
"AM",
"AN",
"BG",
"BH",
"BI",
"BK",
"BL",
"BO",
"CF",
"CJ",
"DP",
"ED",
"EI",
"EJ",
"EM",
"EN",
"EP",
"FJ",
"GH",
"GK",
"HC",
"HF",
"HJ",
"HK",
"ID",
"IJ",
"IL",
"IO",
"IP",
"JD",
"JP",
"LO",
"MN"
] | {"A": [98.0, 186.0], "B": [49.0, 72.0], "C": [222.0, 128.0], "D": [147.0, 0.0], "E": [172.0, 187.0], "F": [0.0, 129.0], "G": [24.0, 15.0], "H": [73.0, 129.0], "I": [157.0, 72.0], "J": [164.0, 128.0], "K": [118.0, 233.0], "L": [224.0, 72.0], "M": [0.0, 185.0], "N": [222.0, 187.0], "O": [1.0, 72.0], "P": [177.0, 226.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, F)), 3y)
- 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))
-
If $\overline{PR} \| \over... | 12 | [
"Parallel(Line(P,R),Line(K,L))",
"Equals(LengthOf(Line(K,N)),9)",
"Equals(LengthOf(Line(L,N)),16)",
"Equals(LengthOf(Line(P,M)),Mul(Line(K,P),2))",
"Find(LengthOf(Line(M,N)))"
] | [
"Equals(LengthOf(Line(E, F)), 3y)",
"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]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(L, M)), 10)
- Equals(LengthOf(Line(N, M)), 10)
- Equals(LengthOf(Line(P, L)), 2x-4)
- Equals(LengthOf(Line(P, N)), x+5)
- PointLiesOnLine(M, Line(N, L))
- PointLiesOnLine(P, Line(M, A))
- Perpendicular(Line(N, M), Line(P, M))
Find $NP$. | 14 | [
"Find(LengthOf(Line(N,P)))"
] | [
"Equals(LengthOf(Line(L, M)), 10)",
"Equals(LengthOf(Line(N, M)), 10)",
"Equals(LengthOf(Line(P, L)), 2x-4)",
"Equals(LengthOf(Line(P, N)), x+5)",
"PointLiesOnLine(M, Line(N, L))",
"PointLiesOnLine(P, Line(M, A))",
"Perpendicular(Line(N, M), Line(P, M))"
] | [
"PN",
"PL",
"PM",
"PA",
"NL",
"NM",
"LM",
"MA"
] | {"P": [147.88318484595644, 187.23386750050497], "N": [293.40285204991085, 0.6730398261421584], "L": [3.1128586096515107, 1.9969438908014752], "M": [150.98249743496893, 0.9932705655139102], "A": [147.0, 227.0]} | [] |
Diagram Logic Form:
- PointLiesOnLine(M, Line(L, J))
In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=34$, find $m \angle JPM$. | 36.5 | [
"Equals(LengthOf(Line(J,M)),Line(P,M))",
"Equals(LengthOf(Line(M,L)),Line(P,L))",
"Equals(MeasureOf(Angle(P,L,J)),34)",
"Find(MeasureOf(Angle(J,P,M)))"
] | [
"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(LengthOf(Line(Y, X)), 15)
- Equals(LengthOf(Line(Y, Q)), x)
- Equals(LengthOf(Line(M, P)), 16)
- Equals(LengthOf(Line(M, K)), 20)
- PointLiesOnLine(P, Line(L, K))
- PointLiesOnLine(Q, Line(Z, X))
- Perpendicular(Line(P, L), Line(M, P))
- Perpendicular(Line(Y, Q), Line(Q, Z))
- Equals(Measur... | 12 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(Y, X)), 15)",
"Equals(LengthOf(Line(Y, Q)), x)",
"Equals(LengthOf(Line(M, P)), 16)",
"Equals(LengthOf(Line(M, K)), 20)",
"PointLiesOnLine(P, Line(L, K))",
"PointLiesOnLine(Q, Line(Z, X))",
"Perpendicular(Line(P, L), Line(M, P))",
"Perpendicular(Line(Y, Q), Line(Q, Z))",
"Equals... | [
"MK",
"MP",
"ML",
"PK",
"PL",
"LK",
"YZ",
"YQ",
"YX",
"ZQ",
"QX",
"ZX"
] | {"K": [2.0, 1.0], "M": [110.0, 324.0], "P": [107.0, 1.0], "L": [319.0, 0.0], "Z": [350.0, 250.0], "Q": [500.0, 250.0], "X": [570.0, 250.0], "Y": [500.0, 10.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(A, B, D)), 130)
- Equals(MeasureOf(Angle(C, B, A)), x)
- Equals(MeasureOf(Angle(D, B, C)), 95)
- PointLiesOnCircle(A, Circle(B, radius_1_0))
- PointLiesOnCircle(C, Circle(B, radius_1_0))
- PointLiesOnCircle(D, Circle(B, radius_1_0))
Find $x$. | 135 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(A, B, D)), 130)",
"Equals(MeasureOf(Angle(C, B, A)), x)",
"Equals(MeasureOf(Angle(D, B, C)), 95)",
"PointLiesOnCircle(A, Circle(B, radius_1_0))",
"PointLiesOnCircle(C, Circle(B, radius_1_0))",
"PointLiesOnCircle(D, Circle(B, radius_1_0))"
] | [
"AB",
"BC",
"BD"
] | {"A": [156.0, 1.0], "B": [158.0, 158.0], "C": [47.0, 267.0], "D": [279.0, 256.0]} | [
"B"
] |
Diagram Logic Form:
- PointLiesOnLine(U, Line(T, P))
- PointLiesOnLine(A, Line(T, R))
- PointLiesOnLine(Q, Line(R, P))
If $\overline{RQ} \cong \overline{RS}$ and $ m ∠RQS = 75 $, find $ m ∠R $. | 30 | [
"Equals(LengthOf(Line(R,Q)),Line(R,S))",
"Equals(MeasureOf(Angle(R,Q,S)),75)",
"Find(MeasureOf(Angle(R)))"
] | [
"PointLiesOnLine(U, Line(T, P))",
"PointLiesOnLine(A, Line(T, R))",
"PointLiesOnLine(Q, Line(R, P))"
] | [
"AQ",
"AR",
"AT",
"AU",
"QP",
"QR",
"RP",
"TP",
"TR",
"UP",
"UQ",
"UT"
] | {"A": [181.0, 90.0], "P": [0.0, 228.0], "Q": [81.0, 90.0], "R": [131.0, 2.0], "T": [263.0, 228.0], "U": [131.0, 227.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(G, O, I)), 3y+1)
- Equals(MeasureOf(Angle(O, I, E)), 4x-5)
- Equals(MeasureOf(Angle(I, B, H)), 3x+11)
- PointLiesOnLine(O, Line(G, H))
- PointLiesOnLine(I, Line(E, B))
- Parallel(Line(G,E), Line(O,I))
- Parallel(Line(O,I), Line(H,B))
- Parallel(Line(G,E), Line(O,I))
- Parall... | 40 | [
"Find(y)"
] | [
"Equals(MeasureOf(Angle(G, O, I)), 3y+1)",
"Equals(MeasureOf(Angle(O, I, E)), 4x-5)",
"Equals(MeasureOf(Angle(I, B, H)), 3x+11)",
"PointLiesOnLine(O, Line(G, H))",
"PointLiesOnLine(I, Line(E, B))",
"Parallel(Line(G,E), Line(O,I))",
"Parallel(Line(O,I), Line(H,B))",
"Parallel(Line(G,E), Line(O,I))",
... | [
"EB",
"EI",
"GE",
"GH",
"GO",
"HB",
"IB",
"OH",
"OI"
] | {"A": [195.0, 8.0], "B": [471.0, 148.0], "C": [50.0, 91.0], "D": [285.0, 145.0], "E": [387.0, 7.0], "F": [232.0, 77.0], "G": [1.0, 6.0], "H": [87.0, 146.0], "I": [428.0, 78.0], "J": [398.0, 146.0], "K": [303.0, 6.0], "L": [229.0, 146.0], "M": [455.0, 122.0], "N": [285.0, 78.0], "O": [41.0, 75.0], "P": [71.0, 122.0], "Q... | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, F, E)), 85)
- Equals(MeasureOf(Angle(C, D, F)), 65)
- Equals(MeasureOf(Angle(C, E, F)), x)
- PointLiesOnLine(F, Line(A, D))
- PointLiesOnLine(E, Line(D, C))
Find x to the nearest tenth. | 150 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(D, F, E)), 85)",
"Equals(MeasureOf(Angle(C, D, F)), 65)",
"Equals(MeasureOf(Angle(C, E, F)), x)",
"PointLiesOnLine(F, Line(A, D))",
"PointLiesOnLine(E, Line(D, C))"
] | [
"AD",
"AF",
"DC",
"DE",
"DF",
"EC",
"FE"
] | {"A": [284.0, 0.0], "C": [6.0, 235.0], "D": [347.0, 238.0], "E": [100.0, 237.0], "F": [296.0, 46.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, D)), LengthOf(h))
- Equals(MeasureOf(Angle(C, A, B)), 60)
- Equals(LengthOf(Line(A, C)), 12)
- Equals(LengthOf(Line(A, B)), LengthOf(Line(B, C)))
- PointLiesOnLine(D, Line(A, C))
- Perpendicular(Line(B,C), Line(A,B))
-
Find $h$ in each triangle. | 6 \sqrt 3 | [
"Triangle($)",
"Find(h)"
] | [
"Equals(LengthOf(Line(B, D)), LengthOf(h))",
"Equals(MeasureOf(Angle(C, A, B)), 60)",
"Equals(LengthOf(Line(A, C)), 12)",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(B, C)))",
"PointLiesOnLine(D, Line(A, C))",
"Perpendicular(Line(B,C), Line(A,B))",
""
] | [
"AB",
"AC",
"AD",
"BC",
"CD"
] | {"A": [180.0, 158.0], "B": [91.0, 1.0], "C": [0.0, 157.0], "D": [45.0, 39.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x-4)
- Equals(LengthOf(Line(A, B)), x)
- Equals(LengthOf(Line(B, C)), 8)
- Perpendicular(Line(A, C), Line(B, C))
Find x. | 10 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x-4)",
"Equals(LengthOf(Line(A, B)), x)",
"Equals(LengthOf(Line(B, C)), 8)",
"Perpendicular(Line(A, C), Line(B, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [147.0, 1.0], "B": [1.483687943262396, 217.77446808510638], "C": [191.83626003023608, 165.71186572082024]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(E, B)), 5y)
- Equals(LengthOf(Line(D, B)), \frac{7}{3}y+8)
- Equals(LengthOf(Line(C, E)), \frac{1}{3}x+2)
- Equals(LengthOf(Line(A, C)), \frac{2}{3}x-4)
- PointLiesOnLine(C, Line(A, E))
- PointLiesOnLine(B, Line(D, E))
- Equals(LengthOf(Line(A, C)), LengthOf(Line(C, E)))
- Equ... | 18 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(E, B)), 5y)",
"Equals(LengthOf(Line(D, B)), \\frac{7}{3}y+8)",
"Equals(LengthOf(Line(C, E)), \\frac{1}{3}x+2)",
"Equals(LengthOf(Line(A, C)), \\frac{2}{3}x-4)",
"PointLiesOnLine(C, Line(A, E))",
"PointLiesOnLine(B, Line(D, E))",
"Equals(LengthOf(Line(A, C)), LengthOf(Line(C, E)))",... | [
"AC",
"AD",
"AE",
"CB",
"CE",
"DB",
"DE",
"EB"
] | {"A": [95.0, 270.0], "B": [140.0, 46.0], "C": [49.0, 138.0], "D": [273.0, 91.0], "E": [1.0, 0.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), \frac{8}{9})
- Equals(LengthOf(Line(B, C)), \frac{4}{9})
- Equals(LengthOf(Line(A, C)), x)
- Perpendicular(Line(B, C), Line(A, C))
Find x. | \frac { 4 } { 9 } \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), \\frac{8}{9})",
"Equals(LengthOf(Line(B, C)), \\frac{4}{9})",
"Equals(LengthOf(Line(A, C)), x)",
"Perpendicular(Line(B, C), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [112.0, 222.0], "B": [2.0, 1.0], "C": [1.0, 224.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(N, E)), 18)
- Equals(LengthOf(Line(Q, P)), 26)
- Perpendicular(Line(B, E), Line(D, E))
- PointLiesOnLine(E, Line(Q, P))
- Perpendicular(Line(Q, E), Line(P, E))
Trapezoid MNPQ has an area of 360 square feet. Find the length of $\overline{MN}$. | 14 | [
"Equals(AreaOf(Trapezoid(M,N,P,Q)),360)",
"Find(LengthOf(Line(M,N)))"
] | [
"Equals(LengthOf(Line(N, E)), 18)",
"Equals(LengthOf(Line(Q, P)), 26)",
"Perpendicular(Line(B, E), Line(D, E))",
"PointLiesOnLine(E, Line(Q, P))",
"Perpendicular(Line(Q, E), Line(P, E))"
] | [
"MN",
"MQ",
"NP",
"QP",
"NE",
"QE",
"PE"
] | {"M": [23.0, 3.0], "N": [139.0, 2.0], "P": [248.0, 120.0], "Q": [0.0, 117.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(B, C, A)), 96)
- Equals(MeasureOf(Angle(A, B, C)), 39)
- Equals(LengthOf(Line(B, C)), 17)
Find x. Round side measures to the nearest tenth. | 15.1 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(B, C, A)), 96)",
"Equals(MeasureOf(Angle(A, B, C)), 39)",
"Equals(LengthOf(Line(B, C)), 17)"
] | [
"AB",
"AC",
"BC"
] | {"A": [1.999897614415893, 2.0086686461212935], "B": [0.0, 257.0], "C": [113.04373694609089, 113.37160598362969]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(F, E)), 8)
- Equals(LengthOf(Line(A, B)), x+1)
- Equals(LengthOf(Line(C, D)), x-1)
- Equals(LengthOf(Line(H, G)), 5)
- Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(E, H, G)))
- Equals(MeasureOf(Angle(A, D, C)), MeasureOf(Angle(H, G, F)))
- Equals(MeasureOf(Angle(B, C, D))... | \frac { 10 } { 3 } | [
"Similar(Polygon($1),Polygon($2))",
"Find(LengthOf(Line(C,D)))"
] | [
"Equals(LengthOf(Line(F, E)), 8)",
"Equals(LengthOf(Line(A, B)), x+1)",
"Equals(LengthOf(Line(C, D)), x-1)",
"Equals(LengthOf(Line(H, G)), 5)",
"Equals(MeasureOf(Angle(B, A, D)), MeasureOf(Angle(E, H, G)))",
"Equals(MeasureOf(Angle(A, D, C)), MeasureOf(Angle(H, G, F)))",
"Equals(MeasureOf(Angle(B, C, D)... | [
"AB",
"AD",
"BC",
"CD",
"EF",
"FG",
"HE",
"HG"
] | {"E": [0.0, 17.0], "F": [145.0, 1.0], "G": [90.0, 149.0], "H": [2.0, 168.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(K, J)), 4)
- Equals(MeasureOf(Angle(L, K, J)), 53)
- PointLiesOnCircle(L, Circle(K, radius_1_0))
- PointLiesOnCircle(J, Circle(K, radius_1_0))
Find the area of the shaded sector. Round to the nearest tenth. | 7.4 | [
"Find(AreaOf(Shaded(Sector($))))"
] | [
"Equals(LengthOf(Line(K, J)), 4)",
"Equals(MeasureOf(Angle(L, K, J)), 53)",
"PointLiesOnCircle(L, Circle(K, radius_1_0))",
"PointLiesOnCircle(J, Circle(K, radius_1_0))"
] | [
"KJ",
"LK"
] | {"J": [10.0, 145.0], "K": [108.0, 102.0], "L": [79.0, 206.0]} | [
"K"
] |
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, ... | 50 | [
"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,I,H)))"
] | [
"Equals(MeasureOf(Angle(Y, Z, I)), 20)",
"Equals(MeasureOf(Angle(W, X, J)), 130)",
"PointLiesOnLine(H, Line(G, I))",
"PointLiesOnLine(H, Line(G, Z))",
"PointLiesOnLine(I, Line(H, Z))",
"PointLiesOnLine(I, Line(G, Z))",
"PointLiesOnLine(H, Line(J, X))",
"PointLiesOnLine(I, Line(J, Y))",
"PointLiesOnL... | [
"GH",
"GI",
"GZ",
"HI",
"HX",
"HZ",
"IY",
"IZ",
"JH",
"JI",
"JX",
"JY",
"WX",
"WY",
"WZ",
"XY",
"XZ",
"YZ"
] | {"C": [544.0, 199.0], "D": [0.0, 199.0], "G": [198.0, 103.0], "H": [235.0, 116.0], "I": [401.0, 186.0], "J": [331.0, 2.0], "W": [78.0, 202.0], "X": [163.0, 200.0], "Z": [455.0, 199.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(Q, Line(W, A))
- PointLiesOnLine(X, Line(W, P))
- PointLiesOnLine(P, Line(H, A))
- PointLiesOnLine(X, Line(H, Q))
-
If $\overline{W P}$ is a perpendicular bisector, $m \angle WHA=8 q+17$, $m \angle HWP=10+q$, $AP=6 r+4$, and $PH=22+3 r$, find $q$. | 7 | [
"IsPerpendicularBisectorOf(Line(W,P),Line($))",
"Equals(MeasureOf(Angle(W,H,A)),8q+17)",
"Equals(MeasureOf(Angle(H,W,P)),10+q)",
"Equals(LengthOf(Line(A,P)),6r+4)",
"Equals(LengthOf(Line(P,H)),22+3r)",
"Find(q)"
] | [
"PointLiesOnLine(Q, Line(W, A))",
"PointLiesOnLine(X, Line(W, P))",
"PointLiesOnLine(P, Line(H, A))",
"PointLiesOnLine(X, Line(H, Q))",
""
] | [
"HA",
"HP",
"HQ",
"PA",
"QA",
"WA",
"WH",
"WP",
"WQ",
"XH",
"XP",
"XQ",
"XW"
] | {"A": [210.0, 125.0], "H": [134.0, 1.0], "P": [172.0, 63.0], "Q": [161.0, 136.0], "W": [1.0, 167.0], "X": [148.0, 77.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(J, A)), x)
- Equals(LengthOf(Line(L, K)), 10)
- PointLiesOnLine(A, Line(K, L))
- PointLiesOnCircle(R, Circle(J, radius_0_0))
- PointLiesOnCircle(K, Circle(J, radius_0_0))
- PointLiesOnCircle(L, Circle(J, radius_0_0))
Find x | 5 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(J, A)), x)",
"Equals(LengthOf(Line(L, K)), 10)",
"PointLiesOnLine(A, Line(K, L))",
"PointLiesOnCircle(R, Circle(J, radius_0_0))",
"PointLiesOnCircle(K, Circle(J, radius_0_0))",
"PointLiesOnCircle(L, Circle(J, radius_0_0))"
] | [
"AK",
"AL",
"JA",
"JR",
"KL"
] | {"A": [12.0, 89.0], "J": [88.0, 86.0], "K": [12.0, 126.0], "L": [13.0, 48.0], "R": [155.0, 143.0]} | [
"J"
] |
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))
$a=14, b=48,$ and $c=50$ find $cosB$ | 0.28 | [
"Equals(a,14)",
"Equals(b,48)",
"Equals(c,50)",
"Find(CosOf(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(LengthOf(Line(A, C)), 27)
- Equals(LengthOf(Line(B, A)), 2x+5)
- Equals(LengthOf(Line(B, C)), 3x-4)
- Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))
Find $x$. | 9 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, C)), 27)",
"Equals(LengthOf(Line(B, A)), 2x+5)",
"Equals(LengthOf(Line(B, C)), 3x-4)",
"Equals(LengthOf(Line(B, A)), LengthOf(Line(B, C)))"
] | [
"BA",
"BC",
"AC"
] | {"B": [130.9832285115304, 190.00590813798362], "A": [1.2323029956115477, 1.1560770845258475], "C": [349.0, 191.0]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, A)), 2x+4)
- Equals(LengthOf(Line(C, A)), 3x-1)
- Equals(LengthOf(Line(B, C)), 4x-8)
$\triangle ABC$ is an isosceles triangle with base $BC$. What is the perimeter of the triangle? | 40 | [
"Isosceles(Triangle(A,B,C))",
"Equals(Line(B,C),BaseOf(Isosceles(Triangle(A,B,C))))",
"Find(PerimeterOf(Triangle($)))"
] | [
"Equals(LengthOf(Line(B, A)), 2x+4)",
"Equals(LengthOf(Line(C, A)), 3x-1)",
"Equals(LengthOf(Line(B, C)), 4x-8)"
] | [
"BA",
"BC",
"CA"
] | {"A": [199.0, 0.0], "B": [0.0, 280.0], "C": [398.0, 280.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, T)), 13)
- Equals(LengthOf(Line(X, Y)), 7)
- Equals(MeasureOf(Angle(Z, X, Y)), 124)
- PointLiesOnLine(Y, Line(R, T))
- PointLiesOnLine(X, Line(R, S))
- PointLiesOnLine(Z, Line(T, S))
$\overline{XY}$ and $\overline{XZ}$ are midsegments of $\triangle RST$. Find $m \angle RYX... | 124 | [
"IsMidsegmentOf(Line(X,Y),Triangle(R,S,T))",
"IsMidsegmentOf(Line(X,Z),Triangle(R,S,T))",
"Find(MeasureOf(Angle(R,Y,X)))"
] | [
"Equals(LengthOf(Line(R, T)), 13)",
"Equals(LengthOf(Line(X, Y)), 7)",
"Equals(MeasureOf(Angle(Z, X, Y)), 124)",
"PointLiesOnLine(Y, Line(R, T))",
"PointLiesOnLine(X, Line(R, S))",
"PointLiesOnLine(Z, Line(T, S))"
] | [
"RS",
"RT",
"RX",
"RY",
"SX",
"SZ",
"TS",
"TY",
"TZ",
"XY",
"XZ"
] | {"R": [1.0, 325.0], "S": [535.0, 1.0], "T": [385.0, 326.0], "X": [273.0, 160.0], "Y": [158.0, 325.0], "Z": [461.0, 162.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, D)), 6)
- Equals(LengthOf(Line(B, E)), 5)
- Equals(LengthOf(Line(A, E)), x)
- PointLiesOnLine(E, Line(A, B))
- PointLiesOnCircle(B, Circle(C, radius_4_0))
- PointLiesOnCircle(D, Circle(C, radius_4_0))
- PointLiesOnCircle(E, Circle(C, radius_4_0))
Find x. Assume that segmen... | 4 | [
"Tangent(Line($),Circle($))",
"Find(x)"
] | [
"Equals(LengthOf(Line(A, D)), 6)",
"Equals(LengthOf(Line(B, E)), 5)",
"Equals(LengthOf(Line(A, E)), x)",
"PointLiesOnLine(E, Line(A, B))",
"PointLiesOnCircle(B, Circle(C, radius_4_0))",
"PointLiesOnCircle(D, Circle(C, radius_4_0))",
"PointLiesOnCircle(E, Circle(C, radius_4_0))"
] | [
"AB",
"AD",
"AE",
"BE"
] | {"A": [197.0, 71.0], "B": [4.0, 71.0], "C": [55.0, 51.0], "D": [99.0, 16.0], "E": [104.0, 71.0]} | [
"C"
] |
Diagram Logic Form:
- Equals(LengthOf(Line(R, S)), 10)
- Equals(LengthOf(Line(R, Q)), 12)
- Equals(LengthOf(Line(R, Z)), x)
- Equals(LengthOf(Line(A, Z)), y)
- Equals(LengthOf(Line(Q, Z)), z)
- Equals(MeasureOf(Angle(S, P, A)), 45)
- Equals(MeasureOf(Angle(A, Q, R)), 30)
- PointLiesOnLine(A, Line(P, Z))
- PointLiesOnLi... | 38 + 6 \sqrt { 2 } + 6 \sqrt { 3 } | [
"Find(PerimeterOf(Trapezoid(P,Q,R,S)))"
] | [
"Equals(LengthOf(Line(R, S)), 10)",
"Equals(LengthOf(Line(R, Q)), 12)",
"Equals(LengthOf(Line(R, Z)), x)",
"Equals(LengthOf(Line(A, Z)), y)",
"Equals(LengthOf(Line(Q, Z)), z)",
"Equals(MeasureOf(Angle(S, P, A)), 45)",
"Equals(MeasureOf(Angle(A, Q, R)), 30)",
"PointLiesOnLine(A, Line(P, Z))",
"PointL... | [
"AQ",
"AZ",
"PA",
"PQ",
"PZ",
"RQ",
"RZ",
"SA",
"SP",
"SR",
"ZQ"
] | {"A": [160.0, 184.0], "P": [1.0, 185.0], "Q": [730.0, 183.0], "R": [420.0, 6.0], "S": [160.0, 8.0], "Z": [421.0, 185.0]} | [
""
] |
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... | 99 | [
"Find(MeasureOf(Angle(3)))"
] | [
"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:
- Equals(MeasureOf(Angle(S, T, Q)), x)
- Equals(MeasureOf(Angle(T, Q, R)), 2x+5)
- Equals(MeasureOf(Angle(R, S, T)), 2x+7)
- Equals(MeasureOf(Angle(Q, R, S)), x)
Find $m\angle S$ | 123 | [
"Find(MeasureOf(Angle(S)))"
] | [
"Equals(MeasureOf(Angle(S, T, Q)), x)",
"Equals(MeasureOf(Angle(T, Q, R)), 2x+5)",
"Equals(MeasureOf(Angle(R, S, T)), 2x+7)",
"Equals(MeasureOf(Angle(Q, R, S)), x)"
] | [
"RQ",
"SR",
"ST",
"TQ"
] | {"Q": [176.0, 3.0], "R": [0.0, 144.0], "S": [214.0, 241.0], "T": [382.0, 147.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(A, B)), 12)
- Equals(LengthOf(Line(A, C)), x)
- Equals(MeasureOf(Angle(A, B, C)), 30)
- Equals(MeasureOf(Angle(B, C, A)), 60)
- Equals(LengthOf(Line(B, C)), y)
- Perpendicular(Line(A, B), Line(A, C))
Find x. | 4 \sqrt { 3 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(A, B)), 12)",
"Equals(LengthOf(Line(A, C)), x)",
"Equals(MeasureOf(Angle(A, B, C)), 30)",
"Equals(MeasureOf(Angle(B, C, A)), 60)",
"Equals(LengthOf(Line(B, C)), y)",
"Perpendicular(Line(A, B), Line(A, C))"
] | [
"AB",
"AC",
"BC"
] | {"A": [237.41694744931135, 0.14479517644971907], "B": [-2.842170943040401e-14, 138.0], "C": [319.13798291808644, 141.32837692319038]} | [] |
Diagram Logic Form:
- Equals(LengthOf(Line(B, C)), 4x-17)
- Equals(MeasureOf(Angle(C, B, F)), 3y+5)
- Equals(MeasureOf(Angle(D, F, B)), 5y-13)
- Equals(LengthOf(Line(D, F)), 2x-1)
-
Find $y$ so that the quadrilateral is a parallelogram. | 9 | [
"Parallelogram($)",
"Find(y)"
] | [
"Equals(LengthOf(Line(B, C)), 4x-17)",
"Equals(MeasureOf(Angle(C, B, F)), 3y+5)",
"Equals(MeasureOf(Angle(D, F, B)), 5y-13)",
"Equals(LengthOf(Line(D, F)), 2x-1)",
""
] | [
"BC",
"CF",
"FD",
"DB",
"BF"
] | {"B": [1.0, 0.0], "C": [334.0, 2.0], "D": [1.0, 202.0], "F": [335.0, 201.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(C, X, B)), 135)
- Equals(MeasureOf(Angle(A, X, C)), 118)
- Equals(MeasureOf(Angle(A, X, B)), x)
- PointLiesOnCircle(A, Circle(X, radius_2_0))
- PointLiesOnCircle(B, Circle(X, radius_2_0))
- PointLiesOnCircle(C, Circle(X, radius_2_0))
Find $x$. | 107 | [
"Find(x)"
] | [
"Equals(MeasureOf(Angle(C, X, B)), 135)",
"Equals(MeasureOf(Angle(A, X, C)), 118)",
"Equals(MeasureOf(Angle(A, X, B)), x)",
"PointLiesOnCircle(A, Circle(X, radius_2_0))",
"PointLiesOnCircle(B, Circle(X, radius_2_0))",
"PointLiesOnCircle(C, Circle(X, radius_2_0))"
] | [
"AX",
"XB",
"XC"
] | {"A": [313.0, 156.0], "B": [86.0, 18.0], "C": [114.0, 306.0], "X": [158.0, 157.0]} | [
"X"
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(D, F, H)), MeasureOf(Angle(11)))
- Equals(MeasureOf(Angle(K, F, A)), MeasureOf(Angle(12)))
-
$m∠11 = 4x$, $m∠12 = 2x -6 $. Find the measure of $\angle 12$. | 56 | [
"Equals(MeasureOf(Angle(11)),4x)",
"Equals(MeasureOf(Angle(12)),2x-6)",
"Find(MeasureOf(Angle(12)))"
] | [
"Equals(MeasureOf(Angle(D, F, H)), MeasureOf(Angle(11)))",
"Equals(MeasureOf(Angle(K, F, A)), MeasureOf(Angle(12)))",
""
] | [
"BF",
"BK",
"DA",
"DF",
"FA",
"FK"
] | {"A": [307.0, 106.0], "B": [31.0, 101.0], "D": [17.0, 10.0], "F": [163.0, 58.0], "H": [316.0, 16.0]} | [
""
] |
Diagram Logic Form:
- Equals(MeasureOf(Angle(V, T, U)), 74)
- Equals(LengthOf(Line(T, V)), LengthOf(Line(T, U)))
Find $m \angle TUV$ | 53 | [
"Find(MeasureOf(Angle(T,U,V)))"
] | [
"Equals(MeasureOf(Angle(V, T, U)), 74)",
"Equals(LengthOf(Line(T, V)), LengthOf(Line(T, U)))"
] | [
"TU",
"TV",
"VU"
] | {"T": [244.0, 0.0], "U": [2.0, 180.0], "V": [350.0, 284.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(V, W)), 3x-6)
- Equals(LengthOf(Line(Y, W)), 5)
- Equals(LengthOf(Line(Z, W)), 6)
- Equals(LengthOf(Line(W, X)), x+4)
- PointLiesOnLine(W, Line(Z, Y))
- PointLiesOnLine(W, Line(V, X))
Find x | 6 | [
"Find(x)"
] | [
"Equals(LengthOf(Line(V, W)), 3x-6)",
"Equals(LengthOf(Line(Y, W)), 5)",
"Equals(LengthOf(Line(Z, W)), 6)",
"Equals(LengthOf(Line(W, X)), x+4)",
"PointLiesOnLine(W, Line(Z, Y))",
"PointLiesOnLine(W, Line(V, X))"
] | [
"VW",
"VX",
"WX",
"YW",
"YX",
"ZV",
"ZW",
"ZY"
] | {"V": [0.0, 0.0], "W": [149.0, 95.0], "X": [271.0, 173.0], "Y": [228.0, 28.0], "Z": [54.0, 179.0]} | [
""
] |
Diagram Logic Form:
- Equals(LengthOf(Line(C, B)), 72)
- Equals(LengthOf(Line(C, A)), z)
- Equals(LengthOf(Line(P, B)), 8y)
- Equals(LengthOf(Line(P, A)), y)
- Equals(LengthOf(Line(A, B)), x)
- PointLiesOnLine(P, Line(C, B))
- Perpendicular(Line(C, P), Line(P, A))
Find x | 4 \sqrt { 6 } | [
"Find(x)"
] | [
"Equals(LengthOf(Line(C, B)), 72)",
"Equals(LengthOf(Line(C, A)), z)",
"Equals(LengthOf(Line(P, B)), 8y)",
"Equals(LengthOf(Line(P, A)), y)",
"Equals(LengthOf(Line(A, B)), x)",
"PointLiesOnLine(P, Line(C, B))",
"Perpendicular(Line(C, P), Line(P, A))"
] | [
"AC",
"AP",
"CB",
"CP",
"AB",
"PB"
] | {"A": [1.0, 112.0], "B": [191.0, 134.0], "C": [0.0, 1.0], "P": [65.0, 46.0]} | [
""
] |
Diagram Logic Form:
- PointLiesOnLine(T, Line(C, A))
- PointLiesOnLine(T, Line(D, B))
- Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))
- Equals(LengthOf(Line(C, B)), LengthOf(Line(C, D)))
If $m\angle BAD = 38$ and $m\angle BCD = 50$, find $m\angle ADC$. | 146 | [
"Equals(MeasureOf(Angle(B,A,D)),38)",
"Equals(MeasureOf(Angle(B,C,D)),50)",
"Find(MeasureOf(Angle(A,D,C)))"
] | [
"PointLiesOnLine(T, Line(C, A))",
"PointLiesOnLine(T, Line(D, B))",
"Equals(LengthOf(Line(A, B)), LengthOf(Line(A, D)))",
"Equals(LengthOf(Line(C, B)), LengthOf(Line(C, D)))"
] | [
"AB",
"AD",
"AT",
"BT",
"CA",
"CB",
"CD",
"CT",
"DB",
"DT"
] | {"A": [-0.0, 165.0], "B": [169.0, 12.0], "C": [287.0, 11.0], "D": [221.0, 111.0], "T": [194.0, 61.0]} | [
""
] |
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)),... | 110 | [
"Find(MeasureOf(Angle(5)))"
] | [
"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(N, A)), 4)
- PointLiesOnCircle(N, Circle(A, radius_1_0))
Find the perimeter or circumference of the figure. Round to the nearest tenth. | 25.1 | [
"Find(PerimeterOf(Shape($)))"
] | [
"Equals(LengthOf(Line(N, A)), 4)",
"PointLiesOnCircle(N, Circle(A, radius_1_0))"
] | [
"NA"
] | {"A": [88.0, 91.0], "N": [157.0, 31.0]} | [
"A"
] |
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