problem stringlengths 7 242 | images images listlengths 1 1 | answer stringlengths 1 34 | prompt stringlengths 629 1.78k | id int64 0 2.1k | responses listlengths 32 32 | extracted_answers listlengths 32 32 | rewards listlengths 32 32 | mean_reward float64 0 1 |
|---|---|---|---|---|---|---|---|---|
Find m \angle Q. | 70 |
You are a step-by-step reasoner for geometry problems.
Follow these guidelines:
1. Write your reasoning clearly and logically, one step per line.
2. End your response with a final answer in the format: **Final Answer: \boxed{}**
---
**Diagram Description Corresponding to the provided image:**
The diagram shows a ... | 2,071 | [
"We are given a quadrilateral QRST with the following information:\n\n- QR = 8\n- ST = 8\n- ∠QRS = 110° (angle at R, between points Q, R, S)\n- Arrows indicate direction: Q → T, R → S, S → T.\n\nWe are to find m∠Q, which is the angle at vertex Q, i.e., ∠RQT or ∠TQR — the interior angle of the quadrilateral at verte... | [
"\\boxed{We are given a quadrilateral QRST with the following information:\n\n- QR = 8\n- ST = 8\n- ∠QRS = 110° (angle at R, between points Q, R, S)\n- Arrows indicate direction: Q → T, R → S, S → T.\n\nWe are to find m∠Q, which is the angle at vertex Q, i.e., ∠RQT or ∠TQR — the interior angle of the quadrilateral ... | [
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Find x so that the quadrilateral is a parallelogram. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 30 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 2,048 | ["To solve for x so that the quadrilateral DHCB is a parallelogram, we need to use properties of par(...TRUNCATED) | ["\\boxed{To solve for x so that the quadrilateral DHCB is a parallelogram, we need to use propertie(...TRUNCATED) | [0.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.125 |
Find the area of the figure in feet. Round to the nearest tenth, if necessary. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 31.2 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 1,481 | ["We are given a diagram of a quadrilateral (possibly a kite or a rhombus) with vertices L, B, C, A,(...TRUNCATED) | ["\\boxed{We are given a diagram of a quadrilateral (possibly a kite or a rhombus) with vertices L, (...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0 |
In \odot G, m \angle A G B = 30 and C G \perp G D. Find m \widehat B C. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 60 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 1,434 | ["We are given:\n\n- Circle centered at G.\n- Points A, B, C, D, F lie on the circle.\n- ∠AGB = 30(...TRUNCATED) | ["\\boxed{\\boxed{60^\\circ}**}","\\boxed{\\boxed{60}**}","\\boxed{\\boxed{}","\\boxed{We are given (...TRUNCATED) | [1.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,1.0,1.0,1.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,1.0,0.0(...TRUNCATED) | 0.46875 |
"Quadrilateral A B C D is a rectangle. If m \\angle A D B = 4 x + 8 and m \\angle D B A = 6 x + 12, (...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 7 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 1,023 | ["We are given that quadrilateral ABCD is a rectangle.\n\nIn a rectangle:\n- All interior angles are(...TRUNCATED) | ["\\boxed{\\boxed{7}**}","\\boxed{\\boxed{7}**}","\\boxed{\\boxed{7}**}","\\boxed{\\boxed{7}**}","\\(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
"In \\odot O, E C and A B are diameters, and \\angle B O D \\cong \\angle D O E \\cong \\angle E O F(...TRUNCATED) | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 90 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 595 | ["We are given a circle centered at O, with diameters EC and AB intersecting at O. Also, OA ⊥ OC i(...TRUNCATED) | ["\\boxed{We are given a circle centered at O, with diameters EC and AB intersecting at O. Also, OA (...TRUNCATED) | [0.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.25 |
Square F G H J is inscribed in \odot K. Find the measure of a central angle. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 90 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 1,129 | ["We are told that square FGHJ is inscribed in circle ⊙K. That means all four vertices F, G, H, J (...TRUNCATED) | ["\\boxed{\\boxed{90^\\circ}**}","\\boxed{\\boxed{90^\\circ}**}","\\boxed{\\boxed{90^\\circ}**}","\\(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
In \odot F, G K = 14 and m \widehat G H K = 142. Find J K. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 7 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 788 | ["We are given a circle ⊙F with radius 7.0, and we are told that MF = 8. But since F is the center(...TRUNCATED) | ["\\boxed{We are given a circle ⊙F with radius 7.0, and we are told that MF = 8. But since F is th(...TRUNCATED) | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) | 0.0625 |
In rhombus A B C D, m \angle D A B = 2, m \angle A D C and C B = 6. Find D A. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 6 | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 145 | ["We are told that ABCD is a **rhombus**, and given:\n\n- CB = 6\n- m∠DAB = 2 × m∠ADC\n- We are(...TRUNCATED) | ["\\boxed{\\boxed{6}**}","\\boxed{\\boxed{6}**}","\\boxed{\\boxed{6}**}","\\boxed{\\boxed{6}**}","\\(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0(...TRUNCATED) | 0.96875 |
Find x. | [{"src":"https://datasets-server.huggingface.co/assets/VLM4Geo/geometry3k-eval-Qwen3-VL-235B-A22B-In(...TRUNCATED) | 4 \sqrt { 29 } | "\nYou are a step-by-step reasoner for geometry problems. \n\n\nFollow these guidelines:\n1. Write y(...TRUNCATED) | 1,169 | ["We are given a quadrilateral ABCD with diagonals AC and BD intersecting at point E.\n\nWe are told(...TRUNCATED) | ["\\boxed{\\boxed{4\\sqrt{29}}**}","\\boxed{\\boxed{4\\sqrt{29}}**}","\\boxed{\\boxed{4\\sqrt{29}}**(...TRUNCATED) | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) | 1 |
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