1509cxt/Geo-TinyLLaVA
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geometry3k/train/0/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "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); "
}
] |
geometry3k/train/2/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(T, Q)), 86); Equals(LengthOf(Line(S, R)), 54); Equals(LengthOf(Line(A, R)), LengthOf(Line(Q, A))); Equals(LengthOf(Line(B, S)), LengthOf(Line(T, B))); PointLiesOnLine(A, Line(Q, R)); PointLiesOnLine(B, Line(T, S)); "
}
] |
geometry3k/train/3/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(W, Z)), 23); Equals(MeasureOf(Angle(Z, W, X)), 112); Equals(LengthOf(Line(X, Y)), 23); Parallel(Line(W, X), Line(Z, Y)); "
}
] |
geometry3k/train/4/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, D)), 10); Equals(LengthOf(Line(B, C)), x); Equals(LengthOf(Line(B, D)), 4); Equals(LengthOf(Line(A, B)), y); Equals(LengthOf(Line(A, D)), z); Perpendicular(Line(C, D), Line(A, C)); Perpendicular(Line(C, B), Line(B, A)); PointLiesOnLine(B, Line(D, A)); "
}
] |
geometry3k/train/6/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, T)), 7\\sqrt{2}); Equals(LengthOf(Line(T, S)), 3\\sqrt{2}); Perpendicular(Line(T, S), Line(R, S)); "
}
] |
geometry3k/train/7/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), \\frac{4}{7}); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(B, C)), \\frac{5}{7}); Perpendicular(Line(A, B), Line(A, C)); "
}
] |
geometry3k/train/8/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(K, J)), 10); Perpendicular(Line(P, M), Line(P, K)); PointLiesOnLine(P, Line(N, M)); PointLiesOnLine(K, Line(P, J)); PointLiesOnLine(P, Line(L, J)); PointLiesOnLine(K, Line(J, L)); PointLiesOnLine(P, Line(K, L)); PointLiesOnCircle(M, Circle(K, radius_)); PointLiesOnCircle(J, Circle(K, radius_)); PointLiesOnCircle(N, Circle(K, radius_)); PointLiesOnCircle(L, Circle(K, radius_)); "
}
] |
geometry3k/train/9/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(B, D)), 10x); Equals(MeasureOf(Arc(F, D)), 40); Equals(MeasureOf(Angle(F, C, D)), x); PointLiesOnLine(F, Line(B, C)); PointLiesOnCircle(B, Circle(E, radius_)); PointLiesOnCircle(D, Circle(E, radius_)); PointLiesOnCircle(F, Circle(E, radius_)); "
}
] |
geometry3k/train/11/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(M, Y), Line(M, A)); Perpendicular(Line(N, D), Line(Z, N)); PointLiesOnLine(N, Line(Z, X)); PointLiesOnLine(M, Line(Y, X)); PointLiesOnLine(N, Line(D, C)); PointLiesOnLine(M, Line(A, B)); PointLiesOnCircle(Z, Circle(X, radius_)); PointLiesOnCircle(A, Circle(X, radius_)); PointLiesOnCircle(C, Circle(X, radius_)); PointLiesOnCircle(D, Circle(X, radius_)); PointLiesOnCircle(Y, Circle(X, radius_)); "
}
] |
geometry3k/train/12/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 5); Equals(LengthOf(Line(E, C)), 4.5); Equals(LengthOf(Line(C, A)), 7.5); Equals(LengthOf(Line(B, D)), x); PointLiesOnLine(C, Line(E, A)); PointLiesOnLine(B, Line(A, D)); PointLiesOnCircle(E, Circle(X, radius_)); PointLiesOnCircle(C, Circle(X, radius_)); PointLiesOnCircle(D, Circle(X, radius_)); PointLiesOnCircle(B, Circle(X, radius_)); "
}
] |
geometry3k/train/13/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 2x+3); Equals(LengthOf(Line(J, D)), 4y); Equals(LengthOf(Line(A, C)), 8y-36); Equals(LengthOf(Line(B, J)), 5x); "
}
] |
geometry3k/train/15/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 10); Equals(LengthOf(Line(A, C)), y); Equals(MeasureOf(Angle(C, B, A)), 60); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(C, A), Line(C, B)); "
}
] |
geometry3k/train/16/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Parallel(Line(E, B), Line(D, C)); PointLiesOnLine(E, Line(D, A)); PointLiesOnLine(B, Line(A, C)); "
}
] |
geometry3k/train/17/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(P, N, M)), MeasureOf(Angle(P, Q, M))); Equals(MeasureOf(Angle(Q, P, N)), MeasureOf(Angle(Q, M, N))); "
}
] |
geometry3k/train/18/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 4x-17); Equals(MeasureOf(Angle(C, B, A)), 3y+3); Equals(LengthOf(Line(C, D)), 2x-1); Equals(MeasureOf(Angle(B, C, D)), 4y-19); "
}
] |
geometry3k/train/19/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 10); Equals(LengthOf(Line(B, A)), 8); Equals(MeasureOf(Angle(A, D, E)), x); Equals(LengthOf(Line(C, B)), 8); Equals(LengthOf(Line(D, C)), 10); Perpendicular(Line(D, E), Line(E, A)); Equals(Line(E, B), Line(A, E)); Equals(Line(E, C), Line(E, B)); PointLiesOnLine(E, Line(B, D)); PointLiesOnLine(E, Line(A, C)); "
}
] |
geometry3k/train/20/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(X, C, A)), y+58); Equals(MeasureOf(Angle(A, B, X)), 5y-6); Equals(MeasureOf(Angle(B, A, C)), 3x-17); Equals(MeasureOf(Angle(B, X, C)), 2x+24); "
}
] |
geometry3k/train/21/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(K, J, E)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(E, J, A)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(K, J, N)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(I, J, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(E, N, H)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(E, N, F)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(H, N, I)), MeasureOf(Angle(8))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(F, N, I))); Parallel(Line(H, F), Line(K, A)); PointLiesOnLine(N, Line(F, H)); PointLiesOnLine(N, Line(J, I)); PointLiesOnLine(N, Line(I, E)); PointLiesOnLine(J, Line(A, K)); PointLiesOnLine(J, Line(E, N)); PointLiesOnLine(J, Line(E, I)); "
}
] |
geometry3k/train/22/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(I, F)), 7); Equals(LengthOf(Line(A, C)), LengthOf(Line(C, E))); Equals(LengthOf(Line(C, E)), LengthOf(Line(I, C))); Equals(LengthOf(Line(D, I)), LengthOf(Line(I, E))); Equals(LengthOf(Line(A, D)), LengthOf(Line(I, D))); PointLiesOnCircle(A, Circle(F, radius_)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(D, Circle(F, radius_)); PointLiesOnCircle(E, Circle(F, radius_)); PointLiesOnCircle(I, Circle(F, radius_)); "
}
] |
geometry3k/train/23/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(T, R)), 2x+7); Equals(LengthOf(Line(S, R)), 3x-5); Equals(LengthOf(Line(T, S)), 22); Equals(LengthOf(Line(T, R)), LengthOf(Line(S, R))); "
}
] |
geometry3k/train/24/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(X, W, Z)), 105); Equals(LengthOf(Line(Y, X)), 24); Equals(LengthOf(Line(Y, Z)), 28); "
}
] |
geometry3k/train/25/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(C, D)), y); Equals(LengthOf(Line(A, B)), x); Equals(LengthOf(Line(D, B)), 9); Equals(LengthOf(Line(D, A)), 3\\sqrt{3}); Equals(MeasureOf(Angle(C, B, A)), 30); Equals(MeasureOf(Angle(A, C, B)), 60); Perpendicular(Line(A, D), Line(C, D)); Perpendicular(Line(B, A), Line(C, A)); PointLiesOnLine(D, Line(C, B)); "
}
] |
geometry3k/train/26/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), y); Equals(LengthOf(Line(C, A)), x); Equals(MeasureOf(Angle(C, B, A)), 30); Equals(LengthOf(Line(B, C)), 18); Perpendicular(Line(C, A), Line(A, B)); "
}
] |
geometry3k/train/27/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(H, P), Line(P, M)); PointLiesOnLine(H, Line(K, J)); PointLiesOnLine(P, Line(L, M)); PointLiesOnLine(H, Line(J, K)); PointLiesOnLine(P, Line(L, M)); PointLiesOnLine(P, Line(K, H)); PointLiesOnCircle(J, Circle(H, radius_)); PointLiesOnCircle(L, Circle(H, radius_)); PointLiesOnCircle(K, Circle(H, radius_)); PointLiesOnCircle(M, Circle(H, radius_)); "
}
] |
geometry3k/train/29/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, S)), 4.5); Equals(MeasureOf(Angle(S, R, T)), x); Equals(LengthOf(Line(T, S)), 3); Equals(LengthOf(Line(T, R)), 6.1); "
}
] |
geometry3k/train/31/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(G, C, E)), x); Equals(MeasureOf(Angle(E, C, A)), 2x); Equals(MeasureOf(Angle(D, C, A)), x); PointLiesOnLine(C, Line(D, G)); "
}
] |
geometry3k/train/32/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, F, H)), MeasureOf(Angle(11))); Equals(MeasureOf(Angle(B, F, A)), MeasureOf(Angle(12))); "
}
] |
geometry3k/train/33/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(E, Line(D, B)); PointLiesOnLine(E, Line(C, A)); "
}
] |
geometry3k/train/34/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(O, A)), 3); Equals(MeasureOf(Angle(A, O, B)), 45); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(B, Circle(O, radius_)); "
}
] |
geometry3k/train/35/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(V, Line(Q, U)); PointLiesOnLine(S, Line(R, T)); "
}
] |
geometry3k/train/36/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "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_)); PointLiesOnCircle(C, Circle(B, radius_)); PointLiesOnCircle(D, Circle(B, radius_)); "
}
] |
geometry3k/train/38/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), y); Equals(MeasureOf(Angle(B, A, C)), 60); Equals(LengthOf(Line(A, C)), 8); Equals(LengthOf(Line(C, B)), x); Perpendicular(Line(A, C), Line(C, B)); "
}
] |
geometry3k/train/40/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 8); Equals(LengthOf(Line(C, B)), 8); Equals(LengthOf(Line(C, A)), 14); Equals(LengthOf(Line(X, B)), x); Perpendicular(Line(X, C), Line(X, B)); PointLiesOnLine(X, Line(C, A)); "
}
] |
geometry3k/train/41/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, L, N)), 25); Equals(LengthOf(Line(M, N)), 4); Perpendicular(Line(L, M), Line(M, N)); Perpendicular(Line(P, N), Line(L, P)); Equals(MeasureOf(Angle(P, L, N)), MeasureOf(Angle(N, L, M))); PointLiesOnLine(M, Line(B, L)); PointLiesOnLine(N, Line(L, A)); PointLiesOnLine(P, Line(L, C)); "
}
] |
geometry3k/train/42/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(G, Line(F, H)); PointLiesOnLine(J, Line(H, K)); "
}
] |
geometry3k/train/43/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(Q, N)), 3x+2); Equals(LengthOf(Line(L, Q)), 12); Equals(LengthOf(Line(M, N)), 2y+5); Equals(LengthOf(Line(Q, R)), 3y); Equals(LengthOf(w), LengthOf(Line(M, L))); Equals(LengthOf(Line(R, M)), 4x-2); PointLiesOnLine(L, Line(Q, M)); PointLiesOnLine(L, Line(R, N)); "
}
] |
geometry3k/train/44/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "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)); "
}
] |
geometry3k/train/45/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(Y, V, W)), 25); Equals(MeasureOf(Arc(Z, X)), 110); Equals(MeasureOf(Arc(Y, W)), x); PointLiesOnLine(Y, Line(V, B)); PointLiesOnLine(Z, Line(V, B)); PointLiesOnLine(X, Line(V, C)); PointLiesOnLine(W, Line(C, V)); PointLiesOnLine(Y, Line(Z, V)); PointLiesOnLine(W, Line(V, X)); PointLiesOnLine(Z, Line(B, Y)); PointLiesOnLine(X, Line(C, W)); PointLiesOnCircle(Y, Circle(A, radius_)); PointLiesOnCircle(Z, Circle(A, radius_)); PointLiesOnCircle(X, Circle(A, radius_)); PointLiesOnCircle(W, Circle(A, radius_)); "
}
] |
geometry3k/train/46/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(K, J)), 11); Equals(MeasureOf(Angle(J, K, L)), 65); PointLiesOnCircle(L, Circle(K, radius_)); PointLiesOnCircle(J, Circle(K, radius_)); "
}
] |
geometry3k/train/47/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, S)), 10); Equals(LengthOf(Line(R, Q)), 12); Equals(LengthOf(Line(Z, R)), x); Equals(LengthOf(Line(A, Z)), y); Equals(LengthOf(Line(Q, Z)), z); Equals(MeasureOf(Angle(A, P, S)), 45); Equals(MeasureOf(Angle(R, Q, A)), 30); Perpendicular(Line(A, P), Line(S, A)); Perpendicular(Line(Z, R), Line(Q, Z)); Parallel(Line(A, Z), Line(R, S)); PointLiesOnLine(A, Line(P, Z)); PointLiesOnLine(A, Line(Q, P)); PointLiesOnLine(Z, Line(Q, A)); PointLiesOnLine(Z, Line(Q, P)); "
}
] |
geometry3k/train/48/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(F, Q, Y)), 4x-5); Equals(MeasureOf(Angle(E, Y, Q)), 3y+1); Equals(MeasureOf(Angle(M, A, Q)), 3x+11); Parallel(Line(E, F), Line(Q, Y)); Parallel(Line(M, A), Line(Q, Y)); Parallel(Line(E, F), Line(M, A)); Parallel(Line(F, A), Line(M, E)); PointLiesOnLine(Y, Line(M, E)); PointLiesOnLine(Q, Line(A, F)); "
}
] |
geometry3k/train/49/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(Y, X, A)), 33); Equals(MeasureOf(Angle(Z, X, W)), 82); PointLiesOnLine(A, Line(X, Z)); PointLiesOnLine(A, Line(Y, W)); "
}
] |
geometry3k/train/50/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(H, G)), 2); Equals(LengthOf(Line(F, G)), 2.5); Equals(LengthOf(Line(F, H)), 4); Equals(LengthOf(Line(E, F)), 6); PointLiesOnLine(F, Line(E, H)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(G, Line(H, C)); "
}
] |
geometry3k/train/51/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(N, W, L)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(E, X, G)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(L, Y, I))); Equals(MeasureOf(Angle(6)), MeasureOf(Angle(Z, Y, L))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(M, Y, K))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(E, Z, K))); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(H, Z, K))); Parallel(Line(G, N), Line(K, I)); Parallel(Line(L, M), Line(E, H)); PointLiesOnLine(X, Line(E, Z)); PointLiesOnLine(Y, Line(Z, I)); PointLiesOnLine(Z, Line(I, K)); PointLiesOnLine(Y, Line(I, K)); PointLiesOnLine(Z, Line(K, Y)); PointLiesOnLine(W, Line(L, M)); PointLiesOnLine(Y, Line(L, M)); PointLiesOnLine(W, Line(Y, L)); PointLiesOnLine(Y, Line(W, M)); PointLiesOnLine(X, Line(N, G)); PointLiesOnLine(W, Line(N, G)); PointLiesOnLine(W, Line(X, G)); PointLiesOnLine(X, Line(W, N)); PointLiesOnLine(Z, Line(X, H)); PointLiesOnLine(Z, Line(H, E)); PointLiesOnLine(X, Line(H, E)); "
}
] |
geometry3k/train/52/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(D, A, B)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(G, D, A))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(F, G, B))); Equals(MeasureOf(Angle(B, C, G)), MeasureOf(Angle(3))); Perpendicular(Line(F, G), Line(F, D)); Perpendicular(Line(G, B), Line(C, B)); Perpendicular(Line(F, G), Line(C, G)); PointLiesOnLine(B, Line(A, G)); PointLiesOnLine(F, Line(D, A)); "
}
] |
geometry3k/train/53/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(E, O, F)), 45); Perpendicular(Line(O, C), Line(A, O)); Perpendicular(Line(O, E), Line(B, O)); PointLiesOnLine(O, Line(B, A)); PointLiesOnLine(O, Line(E, C)); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(C, Circle(O, radius_)); PointLiesOnCircle(F, Circle(O, radius_)); PointLiesOnCircle(E, Circle(O, radius_)); PointLiesOnCircle(B, Circle(O, radius_)); "
}
] |
geometry3k/train/54/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, H)), 12); Equals(LengthOf(Line(B, C)), 8); "
}
] |
geometry3k/train/55/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 10); Equals(LengthOf(Line(A, C)), 6); Equals(LengthOf(Line(B, C)), x); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/56/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(P, A, F)), 33); Equals(LengthOf(Line(A, B)), 10.9); Equals(LengthOf(Line(P, A)), 13); Equals(LengthOf(Line(E, P)), 14.9); Equals(MeasureOf(Angle(D, C, P)), 28.5); Perpendicular(Line(P, B), Line(A, B)); Perpendicular(Line(P, F), Line(F, E)); Perpendicular(Line(D, E), Line(D, P)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(H, Line(E, P)); PointLiesOnLine(I, Line(E, P)); PointLiesOnLine(H, Line(B, E)); PointLiesOnLine(P, Line(B, E)); PointLiesOnLine(I, Line(E, B)); PointLiesOnLine(F, Line(A, E)); PointLiesOnLine(H, Line(E, I)); PointLiesOnLine(P, Line(F, C)); PointLiesOnLine(G, Line(F, J)); PointLiesOnLine(B, Line(A, C)); PointLiesOnLine(P, Line(D, A)); PointLiesOnLine(P, Line(D, J)); PointLiesOnLine(I, Line(H, P)); PointLiesOnLine(P, Line(H, B)); PointLiesOnLine(I, Line(B, H)); PointLiesOnLine(P, Line(I, B)); "
}
] |
geometry3k/train/57/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(A, P), Line(D, P)); PointLiesOnLine(P, Line(A, C)); PointLiesOnLine(P, Line(B, D)); "
}
] |
geometry3k/train/58/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(7)), MeasureOf(Angle(E, D, A))); Equals(MeasureOf(Angle(E, F, B)), 63); Equals(MeasureOf(Angle(F, E, D)), 69); Equals(MeasureOf(Angle(F, B, E)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(B, E, F)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(D, E, G)), 47); Equals(MeasureOf(Angle(E, A, D)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(D, A, G)), 136); Equals(MeasureOf(Angle(C, B, A)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(3)), MeasureOf(Angle(B, E, C))); Equals(MeasureOf(Angle(B, C, E)), MeasureOf(Angle(4))); PointLiesOnLine(E, Line(B, A)); PointLiesOnLine(A, Line(G, B)); PointLiesOnLine(E, Line(B, G)); PointLiesOnLine(A, Line(E, G)); PointLiesOnLine(E, Line(F, C)); "
}
] |
geometry3k/train/60/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, A)), 4); Equals(LengthOf(Line(B, D)), 9); Equals(LengthOf(Line(A, C)), x); Equals(LengthOf(Line(C, D)), z); Equals(LengthOf(Line(C, B)), y); Perpendicular(Line(B, D), Line(D, C)); Perpendicular(Line(C, A), Line(C, B)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/61/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(B, A, C)), 60); Equals(LengthOf(Line(C, A)), 10); Equals(LengthOf(Line(A, B)), 8); Equals(LengthOf(Line(C, B)), LengthOf(a)); "
}
] |
geometry3k/train/62/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(C, E), Line(E, F)); Perpendicular(Line(A, D), Line(D, F)); PointLiesOnLine(E, Line(B, C)); PointLiesOnLine(D, Line(B, A)); PointLiesOnCircle(C, Circle(F, radius_)); PointLiesOnCircle(B, Circle(F, radius_)); PointLiesOnCircle(A, Circle(F, radius_)); "
}
] |
geometry3k/train/63/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, E, D)), 2y); Equals(MeasureOf(Angle(E, D, F)), 110); Equals(MeasureOf(Angle(E, C, F)), 78); Equals(MeasureOf(Angle(D, F, C)), x+36); Parallel(Line(D, F), Line(E, C)); "
}
] |
geometry3k/train/64/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(H, G, A)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(F, H, G)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(A, J, H)), MeasureOf(Angle(3))); Perpendicular(Line(B, H), Line(G, B)); Perpendicular(Line(H, J), Line(G, H)); PointLiesOnLine(A, Line(J, G)); PointLiesOnLine(B, Line(G, J)); PointLiesOnLine(A, Line(J, B)); PointLiesOnLine(B, Line(F, H)); PointLiesOnLine(B, Line(A, G)); PointLiesOnCircle(J, Circle(A, radius_)); PointLiesOnCircle(H, Circle(A, radius_)); PointLiesOnCircle(G, Circle(A, radius_)); PointLiesOnCircle(F, Circle(A, radius_)); "
}
] |
geometry3k/train/65/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, D)), 55); Equals(MeasureOf(Angle(G, B, F)), 35); PointLiesOnLine(B, Line(A, D)); PointLiesOnLine(B, Line(C, G)); PointLiesOnCircle(F, Circle(B, radius_)); PointLiesOnCircle(D, Circle(B, radius_)); PointLiesOnCircle(A, Circle(B, radius_)); PointLiesOnCircle(C, Circle(B, radius_)); PointLiesOnCircle(G, Circle(B, radius_)); "
}
] |
geometry3k/train/66/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, D)), 60); Equals(LengthOf(Line(C, B)), 2x+5); Equals(LengthOf(Line(B, A)), 3x-13); Equals(MeasureOf(Angle(B, C, D)), MeasureOf(Angle(B, D, C))); Equals(MeasureOf(Angle(D, A, B)), MeasureOf(Angle(B, D, A))); "
}
] |
geometry3k/train/67/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(T, Q)), x); Equals(LengthOf(Line(R, Q)), 6); Equals(LengthOf(Line(S, Q)), 18); Equals(LengthOf(Line(R, S)), 14); Equals(MeasureOf(Angle(Q, R, T)), MeasureOf(Angle(S, R, T))); PointLiesOnLine(T, Line(Q, S)); "
}
] |
geometry3k/train/68/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, A)), 5); Equals(LengthOf(Line(C, D)), 12); Equals(LengthOf(Line(B, C)), 31.2); Perpendicular(Line(D, C), Line(B, D)); Perpendicular(Line(B, C), Line(D, C)); PointLiesOnLine(D, Line(B, A)); "
}
] |
geometry3k/train/69/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(1)), MeasureOf(Angle(G, D, E))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(G, D, F))); Equals(MeasureOf(Angle(F, E, D)), 25); Equals(MeasureOf(Angle(D, F, E)), 65); Perpendicular(Line(G, E), Line(D, G)); PointLiesOnLine(G, Line(E, F)); "
}
] |
geometry3k/train/70/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(L, K)), 2); Equals(LengthOf(Line(J, K)), 12); Equals(LengthOf(Line(M, N)), 6); Equals(LengthOf(Line(M, L)), x); PointLiesOnLine(K, Line(J, L)); PointLiesOnLine(M, Line(L, N)); PointLiesOnCircle(J, Circle(A, radius_)); PointLiesOnCircle(M, Circle(A, radius_)); PointLiesOnCircle(N, Circle(A, radius_)); PointLiesOnCircle(K, Circle(A, radius_)); "
}
] |
geometry3k/train/71/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(H, E, F)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(G, E, H)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(F, H, E)), 15x); PointLiesOnLine(H, Line(F, G)); "
}
] |
geometry3k/train/72/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(Z, T, W)), MeasureOf(Angle(4))); Equals(MeasureOf(Angle(T, W, Z)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(Y, W, X)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(Z, T, Y)), MeasureOf(Angle(1))); Equals(MeasureOf(Angle(Z, Y, T)), 52); Equals(MeasureOf(Angle(Z, Y, X)), 38); Perpendicular(Line(W, X), Line(W, T)); Perpendicular(Line(Z, T), Line(Z, Y)); Perpendicular(Line(X, Y), Line(T, Y)); Perpendicular(Line(X, Y), Line(X, W)); PointLiesOnLine(Z, Line(W, Y)); "
}
] |
geometry3k/train/73/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(R, S)), 4); Equals(LengthOf(Line(Q, R)), x); Equals(LengthOf(Line(Q, P)), y); Equals(LengthOf(Line(S, P)), 2); Perpendicular(Line(S, R), Line(S, Q)); Perpendicular(Line(R, Q), Line(P, Q)); PointLiesOnLine(S, Line(P, R)); "
}
] |
geometry3k/train/74/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), 12); Equals(MeasureOf(Angle(C, A, B)), x); Equals(LengthOf(Line(A, B)), y); Perpendicular(Line(B, C), Line(D, B)); Equals(LengthOf(Line(D, A)), LengthOf(Line(D, B))); "
}
] |
geometry3k/train/75/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(U, V, W)), 3x-11); Equals(MeasureOf(Angle(V, U, Z)), x-8); Equals(MeasureOf(Angle(Y, W, V)), x+8); Equals(MeasureOf(Angle(U, Z, Y)), 2x+7); Equals(MeasureOf(Angle(Z, Y, W)), x); "
}
] |
geometry3k/train/76/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, N)), 10); Equals(LengthOf(Line(B, C)), 30); Equals(LengthOf(Line(C, N)), 5); Perpendicular(Line(C, N), Line(A, C)); PointLiesOnLine(C, Line(N, B)); "
}
] |
geometry3k/train/77/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(S, T)), 2y+12); Equals(LengthOf(Line(R, T)), x); Equals(LengthOf(Line(Q, T)), 5y); Equals(LengthOf(Line(T, P)), 5x-28); PointLiesOnLine(T, Line(S, Q)); PointLiesOnLine(T, Line(P, R)); "
}
] |
geometry3k/train/78/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, G, D)), 135); Equals(MeasureOf(Angle(D, G, B)), 145); Equals(MeasureOf(Angle(C, G, E)), x); Equals(MeasureOf(Angle(E, G, B)), x); PointLiesOnCircle(B, Circle(G, radius_)); PointLiesOnCircle(C, Circle(G, radius_)); PointLiesOnCircle(D, Circle(G, radius_)); PointLiesOnCircle(E, Circle(G, radius_)); "
}
] |
geometry3k/train/79/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(F, E)), 4y); Equals(LengthOf(Line(D, E)), 6x-12); Equals(LengthOf(Line(G, F)), 2x+36); Equals(LengthOf(Line(G, D)), 6y-42); "
}
] |
geometry3k/train/80/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), 5); Equals(LengthOf(Line(D, B)), 10); Equals(LengthOf(Line(E, B)), x); Equals(LengthOf(Line(B, C)), 12); PointLiesOnLine(B, Line(D, E)); PointLiesOnLine(B, Line(A, C)); PointLiesOnCircle(D, Circle(O, radius_)); PointLiesOnCircle(A, Circle(O, radius_)); PointLiesOnCircle(C, Circle(O, radius_)); PointLiesOnCircle(E, Circle(O, radius_)); "
}
] |
geometry3k/train/81/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(Q, B')), 8); Equals(LengthOf(Line(B, Q)), 6); Equals(LengthOf(Line(B, B')), x); PointLiesOnLine(D, Line(Q, A)); PointLiesOnLine(B, Line(Q, B')); "
}
] |
geometry3k/train/82/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(G, F, E)), 9x+7); Equals(MeasureOf(Angle(G, D, E)), 5x); Equals(MeasureOf(Angle(D, E, F)), 5x); PointLiesOnLine(F, Line(D, G)); "
}
] |
geometry3k/train/83/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, E)), 12); Equals(LengthOf(Line(C, E)), 17); Equals(LengthOf(Line(E, D)), 17); Equals(LengthOf(Line(B, E)), 12); Perpendicular(Line(A, E), Line(E, D)); PointLiesOnLine(E, Line(A, B)); PointLiesOnLine(E, Line(C, D)); "
}
] |
geometry3k/train/84/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(M, T)), 10-2x); Equals(LengthOf(Line(M, J)), 12-3x); Equals(LengthOf(Line(I, L)), y+4/5); Equals(LengthOf(Line(C, L)), 2y-11/5); Parallel(Line(M, L), Line(T, J)); Parallel(Line(M, L), Line(C, I)); PointLiesOnLine(L, Line(C, J)); PointLiesOnLine(T, Line(A, J)); PointLiesOnLine(J, Line(T, N)); PointLiesOnLine(J, Line(A, N)); PointLiesOnLine(T, Line(N, A)); PointLiesOnLine(M, Line(T, I)); PointLiesOnLine(M, Line(T, P)); PointLiesOnLine(I, Line(C, O)); PointLiesOnLine(J, Line(R, C)); PointLiesOnLine(L, Line(C, R)); PointLiesOnLine(C, Line(O, E)); PointLiesOnLine(I, Line(O, E)); PointLiesOnLine(C, Line(E, I)); PointLiesOnLine(M, Line(Q, I)); PointLiesOnLine(T, Line(Q, I)); PointLiesOnLine(M, Line(L, S)); PointLiesOnLine(J, Line(R, L)); PointLiesOnLine(C, Line(L, U)); PointLiesOnLine(J, Line(U, R)); PointLiesOnLine(L, Line(R, U)); PointLiesOnLine(T, Line(Q, M)); PointLiesOnLine(L, Line(M, V)); PointLiesOnLine(L, Line(S, V)); PointLiesOnLine(M, Line(S, V)); PointLiesOnLine(M, Line(Q, P)); PointLiesOnLine(T, Line(P, Q)); "
}
] |
geometry3k/train/86/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(13)), MeasureOf(Angle(J, A, K))); Equals(MeasureOf(Angle(E, A, K)), MeasureOf(Angle(14))); Equals(MeasureOf(Angle(D, H, F)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(C, I, B)), MeasureOf(Angle(2))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(D, I, C))); Equals(MeasureOf(Angle(E, H, B)), MeasureOf(Angle(8))); Equals(MeasureOf(Angle(10)), MeasureOf(Angle(E, A, C))); Equals(MeasureOf(Angle(G, E, A)), MeasureOf(Angle(15))); Equals(MeasureOf(Angle(F, E, L)), MeasureOf(Angle(12))); Equals(MeasureOf(Angle(A, I, D)), MeasureOf(Angle(5))); Equals(MeasureOf(Angle(9)), MeasureOf(Angle(J, A, C))); Equals(MeasureOf(Angle(A, I, B)), MeasureOf(Angle(6))); Equals(MeasureOf(Angle(G, E, L)), MeasureOf(Angle(16))); Equals(MeasureOf(Angle(11)), MeasureOf(Angle(A, E, F))); Equals(MeasureOf(Angle(7)), MeasureOf(Angle(I, H, E))); Equals(MeasureOf(Angle(B, H, F)), MeasureOf(Angle(4))); Parallel(Line(H, F), Line(C, I)); PointLiesOnLine(I, Line(A, C)); PointLiesOnLine(E, Line(L, A)); PointLiesOnLine(A, Line(K, C)); PointLiesOnLine(I, Line(C, K)); PointLiesOnLine(H, Line(E, F)); PointLiesOnLine(A, Line(E, J)); PointLiesOnLine(H, Line(I, B)); PointLiesOnLine(A, Line(K, I)); PointLiesOnLine(A, Line(J, L)); PointLiesOnLine(E, Line(J, L)); PointLiesOnLine(H, Line(B, D)); PointLiesOnLine(I, Line(D, B)); PointLiesOnLine(I, Line(D, H)); PointLiesOnLine(E, Line(H, G)); PointLiesOnLine(E, Line(G, F)); PointLiesOnLine(H, Line(F, G)); "
}
] |
geometry3k/train/87/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(P, Line(Q, M)); PointLiesOnLine(P, Line(N, R)); "
}
] |
geometry3k/train/89/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(S, A, T)), 93); Equals(MeasureOf(Arc(R, S)), x); Equals(LengthOf(Line(S, R)), LengthOf(Line(T, S))); PointLiesOnCircle(S, Circle(A, radius_)); PointLiesOnCircle(T, Circle(A, radius_)); PointLiesOnCircle(R, Circle(A, radius_)); "
}
] |
geometry3k/train/91/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(D, B)), x-1); Equals(LengthOf(Line(C, E)), x+2); Equals(LengthOf(Line(E, F)), 8); Equals(LengthOf(Line(A, B)), 3); Perpendicular(Line(B, A), Line(C, B)); Perpendicular(Line(D, E), Line(F, E)); PointLiesOnLine(C, Line(D, B)); PointLiesOnLine(G, Line(A, D)); PointLiesOnLine(D, Line(E, B)); PointLiesOnLine(C, Line(B, E)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(G, Line(C, F)); "
}
] |
geometry3k/train/92/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Perpendicular(Line(Y, W), Line(Y, X)); Equals(LengthOf(Line(Y, X)), LengthOf(Line(Z, Y))); PointLiesOnLine(Y, Line(Z, X)); PointLiesOnLine(W, Line(D, Y)); PointLiesOnLine(W, Line(T, D)); PointLiesOnLine(Y, Line(T, D)); PointLiesOnLine(Y, Line(T, W)); "
}
] |
geometry3k/train/93/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, C)), y); Equals(LengthOf(Line(C, D)), 12); Equals(MeasureOf(Angle(D, B, C)), x); Equals(LengthOf(Line(B, D)), 12); Perpendicular(Line(B, D), Line(C, D)); "
}
] |
geometry3k/train/94/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(2)), MeasureOf(Angle(C, D, F))); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(C, H, B))); Equals(MeasureOf(Angle(A, D, F)), 52); Equals(MeasureOf(Angle(E, H, A)), 38); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(C, D, B))); Equals(MeasureOf(Angle(G, B, H)), MeasureOf(Angle(3))); Perpendicular(Line(H, B), Line(D, B)); PointLiesOnLine(D, Line(A, C)); PointLiesOnLine(H, Line(C, A)); PointLiesOnLine(D, Line(A, H)); PointLiesOnLine(H, Line(D, C)); PointLiesOnLine(B, Line(G, D)); PointLiesOnLine(B, Line(E, H)); PointLiesOnLine(D, Line(B, F)); PointLiesOnLine(H, Line(I, B)); PointLiesOnLine(B, Line(I, E)); PointLiesOnLine(H, Line(E, I)); PointLiesOnLine(B, Line(G, F)); PointLiesOnLine(D, Line(G, F)); "
}
] |
geometry3k/train/95/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Arc(B, C)), 170); PointLiesOnCircle(B, Circle(D, radius_)); PointLiesOnCircle(A, Circle(D, radius_)); PointLiesOnCircle(C, Circle(D, radius_)); "
}
] |
geometry3k/train/96/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(P, N, O)), 56); Equals(MeasureOf(Angle(N, B, M)), 70); PointLiesOnCircle(O, Circle(B, radius_)); PointLiesOnCircle(N, Circle(B, radius_)); PointLiesOnCircle(P, Circle(B, radius_)); PointLiesOnCircle(M, Circle(B, radius_)); "
}
] |
geometry3k/train/97/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(C, B, D)), 12x+72); Equals(MeasureOf(Angle(B, C, A)), 3y+36); Equals(MeasureOf(Angle(C, A, D)), 25x+20); Equals(MeasureOf(Angle(A, D, B)), 9y-12); "
}
] |
geometry3k/train/98/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, D)), 11); Equals(LengthOf(Line(B, C)), 25); "
}
] |
geometry3k/train/100/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(P, Q)), 72); Equals(LengthOf(Line(R, Q)), 25); Perpendicular(Line(P, Q), Line(R, Q)); "
}
] |
geometry3k/train/101/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(Y, A)), 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); Perpendicular(Line(B, A), Line(Y, A)); Perpendicular(Line(N, B), Line(A, N)); PointLiesOnLine(N, Line(Y, B)); "
}
] |
geometry3k/train/102/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(K, L)), 6); Equals(MeasureOf(Angle(J, K, L)), 148); PointLiesOnCircle(L, Circle(K, radius_)); PointLiesOnCircle(J, Circle(K, radius_)); "
}
] |
geometry3k/train/103/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(J, K, L)), 2x-11); Equals(MeasureOf(Angle(K, J, L)), 2x+27); Equals(MeasureOf(Angle(K, L, A)), 100); PointLiesOnLine(L, Line(J, A)); "
}
] |
geometry3k/train/104/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(B, A)), c); Equals(MeasureOf(Angle(A, B, C)), 60); Equals(LengthOf(Line(B, C)), a); Equals(MeasureOf(Angle(B, A, C)), 30); Equals(LengthOf(Line(C, A)), b); Perpendicular(Line(A, C), Line(B, C)); "
}
] |
geometry3k/train/105/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, C)), y); Equals(LengthOf(Line(C, B)), 6); Equals(MeasureOf(Angle(C, A, B)), 30); Equals(LengthOf(Line(A, B)), x); Perpendicular(Line(B, C), Line(C, A)); "
}
] |
geometry3k/train/106/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(F, Line(E, A)); PointLiesOnLine(D, Line(E, C)); PointLiesOnLine(P, Line(E, B)); PointLiesOnLine(B, Line(A, C)); PointLiesOnLine(P, Line(A, D)); PointLiesOnLine(P, Line(C, F)); "
}
] |
geometry3k/train/107/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnCircle(P, Circle(U, radius_)); PointLiesOnCircle(S, Circle(U, radius_)); PointLiesOnCircle(Q, Circle(U, radius_)); PointLiesOnCircle(T, Circle(U, radius_)); PointLiesOnCircle(R, Circle(U, radius_)); "
}
] |
geometry3k/train/110/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(P, R, Q)), 115); Perpendicular(Line(R, P), Line(R, N)); PointLiesOnLine(R, Line(M, P)); PointLiesOnCircle(Q, Circle(R, radius_)); PointLiesOnCircle(M, Circle(R, radius_)); PointLiesOnCircle(P, Circle(R, radius_)); PointLiesOnCircle(N, Circle(R, radius_)); "
}
] |
geometry3k/train/111/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(LengthOf(Line(A, B)), 12); Equals(LengthOf(Line(C, B)), x); Equals(MeasureOf(Angle(B, A, C)), 30); Equals(MeasureOf(Angle(B, C, A)), 60); Equals(LengthOf(Line(C, A)), y); Perpendicular(Line(B, C), Line(B, A)); "
}
] |
geometry3k/train/113/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(F, E, A)), MeasureOf(Angle(3))); Equals(MeasureOf(Angle(2)), MeasureOf(Angle(B, A, E))); Equals(MeasureOf(Angle(D, C, A)), 50); Equals(MeasureOf(Angle(1)), MeasureOf(Angle(G, A, D))); Equals(MeasureOf(Angle(F, G, A)), 120); Equals(MeasureOf(Angle(4)), MeasureOf(Angle(F, G, H))); Equals(MeasureOf(Angle(5)), MeasureOf(Angle(F, B, H))); Equals(MeasureOf(Angle(B, F, G)), 56); Equals(MeasureOf(Angle(E, D, C)), 78); PointLiesOnLine(G, Line(B, A)); PointLiesOnLine(B, Line(H, A)); PointLiesOnLine(G, Line(A, H)); PointLiesOnLine(A, Line(C, B)); PointLiesOnLine(G, Line(B, C)); PointLiesOnLine(A, Line(G, C)); PointLiesOnLine(A, Line(H, C)); PointLiesOnLine(B, Line(C, H)); PointLiesOnLine(G, Line(C, H)); PointLiesOnLine(A, Line(D, E)); PointLiesOnLine(G, Line(F, E)); PointLiesOnLine(B, Line(H, G)); "
}
] |
geometry3k/train/115/img_diagram.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "PointLiesOnLine(K, Line(G, J)); PointLiesOnLine(K, Line(F, H)); "
}
] |
geometry3k/train/116/img_diagram_point.png
|
[
{
"from": "human",
"value": "<image>\nPlease use geometric formal language to describe the diagram. Your response could be empty."
},
{
"from": "gpt",
"value": "Equals(MeasureOf(Angle(A, B, C)), 68); Equals(LengthOf(Line(B, C)), x); Equals(MeasureOf(Angle(C, A, B)), 50); Equals(LengthOf(Line(A, C)), 5); "
}
] |
End of preview. Expand
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Size of downloaded dataset files:
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Number of rows:
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Models trained or fine-tuned on 1509cxt/GDF86K