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problem_id string | data_source string | prompt list | ability string | reward_model dict | extra_info dict | images images list |
|---|---|---|---|---|---|---|
geo5k_00000 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, it is known that ∠A=80°, ∠B=60°, and DE∥BC. What is the measure of ∠CED?\nChoices:\nA. 40°\nB. 60°\nC. 120°\nD. 140°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 0,
"answer": "D",
"question": "As shown in the figure, in △ABC, it is known that ∠A=80°, ∠B=60°, and DE∥BC. What is the measure of ∠CED?",
"question_type": "mcq",
"pid": "0",
"choices": [
"40°",
"60°",
"120°",
"140°"
],
"correct_open": "140°",
"answer_exp... | |
geo5k_00001 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB ∥ CD, line EF intersects AB at point E and intersects CD at point F. EG bisects ∠BEF and intersects CD at point G. If ∠1 = 50°, then ∠2 equals ()\nChoices:\nA. 50°\nB. 60°\nC. 65°\nD. 90°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 1,
"answer": "C",
"question": "As shown in the figure, AB ∥ CD, line EF intersects AB at point E and intersects CD at point F. EG bisects ∠BEF and intersects CD at point G. If ∠1 = 50°, then ∠2 equals () Choices: A. 50° B. 60° C. 65° D. 90°",
"question_type": "mcq",
"pid": "1",
... | |
geo5k_00002 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB?\nChoices:\nA. 3cm\nB. 4cm\nC. 6cm\nD. 8cm"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 2,
"answer": "C",
"question": "As shown in the figure, the radii of two concentric circles are 4cm and 5cm respectively. A chord AB of the larger circle is tangent to the smaller circle. What is the length of chord AB?",
"question_type": "mcq",
"pid": "2",
"choices": [
"3c... | |
geo5k_00003 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given that OA = OB = OC and ∠ACB = 30°, what is the measure of ∠AOB?\nChoices:\nA. 40°\nB. 50°\nC. 60°\nD. 70°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 3,
"answer": "C",
"question": "As shown in the figure, given that OA = OB = OC and ∠ACB = 30°, what is the measure of ∠AOB?",
"question_type": "mcq",
"pid": "3",
"choices": [
"40°",
"50°",
"60°",
"70°"
],
"correct_open": "60°",
"answer_explanation": "∵OA=... | |
geo5k_00004 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, line a is perpendicular to line c, and line b is perpendicular to line c. If ∠1 = 70°, then ∠2 = ()\nChoices:\nA. 70°\nB. 90°\nC. 110°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 4,
"answer": "A",
"question": "As shown in the figure, line a is perpendicular to line c, and line b is perpendicular to line c. If ∠1 = 70°, then ∠2 = () Choices: A. 70° B. 90° C. 110° D. 80°",
"question_type": "mcq",
"pid": "4",
"choices": [
"70°",
"90°",
"110°",... | |
geo5k_00005 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given that line a ∥ b, line c intersects a and b at points A and B respectively; and ∠1 = 120°, then ∠2 = ()\nChoices:\nA. 60°\nB. 120°\nC. 30°\nD. 150°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 5,
"answer": "B",
"question": "As shown in the figure, given that line a ∥ b, line c intersects a and b at points A and B respectively; and ∠1 = 120°, then ∠2 = () Choices: A. 60° B. 120° C. 30° D. 150°",
"question_type": "mcq",
"pid": "5",
"choices": [
"60°",
"120°",
... | |
geo5k_00006 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD. If ∠2 = 135°, then the measure of ∠1 is ()\nChoices:\nA. 30°\nB. 45°\nC. 60°\nD. 75°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 6,
"answer": "B",
"question": "As shown in the figure, AB∥CD. If ∠2 = 135°, then the measure of ∠1 is ()\nChoices:\nA. 30°\nB. 45°\nC. 60°\nD. 75°",
"question_type": "mcq",
"pid": "6",
"choices": [
"30°",
"45°",
"60°",
"75°"
],
"correct_open": "45°",
"ans... | |
geo5k_00007 | geo5k | [
{
"role": "user",
"content": "<image>A flower nursery has a plot of land shaped like an isosceles trapezoid ABCD, with the midpoints of its sides being E, F, G, and H, respectively. It is measured that the diagonal AC = 10 meters. Now, they want to use a fence to enclose the quadrilateral EFGH. What is the ... | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 7,
"answer": "C",
"question": "A flower nursery has a plot of land shaped like an isosceles trapezoid ABCD, with the midpoints of its sides being E, F, G, and H, respectively. It is measured that the diagonal AC = 10 meters. Now, they want to use a fence to enclose the quadrilateral... | |
geo5k_00008 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, use the pole BE to measure the height of the tree CD. If the pole BE is 2 meters long, and it is measured that AB=3 meters, AC=9 meters, and points A, E, D are on a straight line, then the tree CD is ()\nChoices:\nA. 6米\nB. 7.5米\nC. 8米\nD. 8.5米"
... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 8,
"answer": "A",
"question": "As shown in the figure, use the pole BE to measure the height of the tree CD. If the pole BE is 2 meters long, and it is measured that AB=3 meters, AC=9 meters, and points A, E, D are on a straight line, then the tree CD is ()",
"question_type": "mcq... | |
geo5k_00009 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure: The perimeter of △ABC is 30 cm. Fold the side AC of △ABC so that vertex C coincides with point A. The crease intersects side BC at point D and intersects side AC at point E. Connect AD. If AE = 4 cm, then the perimeter of △ABD is ()\nChoices:\nA. ... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 9,
"answer": "A",
"question": "As shown in the figure: The perimeter of △ABC is 30 cm. Fold the side AC of △ABC so that vertex C coincides with point A. The crease intersects side BC at point D and intersects side AC at point E. Connect AD. If AE = 4 cm, then the perimeter of △ABD i... | |
geo5k_00010 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, point O is on line AB and OC⊥OD. If ∠COA=36°, then the measure of ∠DOB is ()\nChoices:\nA. 36°\nB. 54°\nC. 64°\nD. 72°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 10,
"answer": "B",
"question": "As shown in the figure, point O is on line AB and OC⊥OD. If ∠COA=36°, then the measure of ∠DOB is ()",
"question_type": "mcq",
"pid": "13",
"choices": [
"36°",
"54°",
"64°",
"72°"
],
"correct_open": "54°",
"answer_explanati... | |
geo5k_00011 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in the parallelogram ABCD with a perimeter of 20 cm, where AB≠AD, AC and BD intersect at point O, and OE⊥BD intersects AD at E, what is the perimeter of △ABE?\nChoices:\nA. 4cm\nB. 6cm\nC. 8cm\nD. 10cm"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 11,
"answer": "D",
"question": "As shown in the figure, in the parallelogram ABCD with a perimeter of 20 cm, where AB≠AD, AC and BD intersect at point O, and OE⊥BD intersects AD at E, what is the perimeter of △ABE?",
"question_type": "mcq",
"pid": "14",
"choices": [
"4cm",... | |
geo5k_00012 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the perimeter of △ABC is 21, and AB=AC, BC=5. The perpendicular bisector DE of AB intersects AB at point D and AC at point E. What is the perimeter of △BEC?\nChoices:\nA. 13\nB. 14\nC. 15\nD. 16"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 12,
"answer": "A",
"question": "As shown in the figure, the perimeter of △ABC is 21, and AB=AC, BC=5. The perpendicular bisector DE of AB intersects AB at point D and AC at point E. What is the perimeter of △BEC?",
"question_type": "mcq",
"pid": "17",
"choices": [
"13",
... | |
geo5k_00013 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the midpoints of the sides of an arbitrary quadrilateral ABCD are E, F, G, and H, respectively. If the lengths of the diagonals AC and BD are both 20 cm, what is the perimeter of quadrilateral EFGH?\nChoices:\nA. 80cm\nB. 40cm\nC. 20cm\nD. 10cm"
... | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 13,
"answer": "B",
"question": "As shown in the figure, the midpoints of the sides of an arbitrary quadrilateral ABCD are E, F, G, and H, respectively. If the lengths of the diagonals AC and BD are both 20 cm, what is the perimeter of quadrilateral EFGH? Choices: A. 80 cm B. 40 cm C... | |
geo5k_00014 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given ∠1 = ∠2 = ∠3 = 55°, what is the degree measure of ∠4?\nChoices:\nA. 110°\nB. 115°\nC. 120°\nD. 125°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 14,
"answer": "D",
"question": "As shown in the figure, given ∠1 = ∠2 = ∠3 = 55°, what is the degree measure of ∠4?",
"question_type": "mcq",
"pid": "22",
"choices": [
"110°",
"115°",
"120°",
"125°"
],
"correct_open": "125°",
"answer_explanation": "试题分析:∵... | |
geo5k_00015 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB is the diameter of circle O, arc BC = arc BD, ∠A = 25°, then the measure of ∠BOD is ()\nChoices:\nA. 25°\nB. 50°\nC. 12.5°\nD. 30°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 15,
"answer": "B",
"question": "As shown in the figure, AB is the diameter of circle O, arc BC = arc BD, ∠A = 25°, then the measure of ∠BOD is ()",
"question_type": "mcq",
"pid": "23",
"choices": [
"25°",
"50°",
"12.5°",
"30°"
],
"correct_open": "50°",
"a... | |
geo5k_00016 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, points A, B, and C are on circle O, ∠A = 50°, then the degree of ∠BOC is ()\nChoices:\nA. 40°\nB. 50°\nC. 80°\nD. 100°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 16,
"answer": "D",
"question": "As shown in the figure, points A, B, and C are on circle O, ∠A = 50°, then the degree of ∠BOC is ()",
"question_type": "mcq",
"pid": "24",
"choices": [
"40°",
"50°",
"80°",
"100°"
],
"correct_open": "100°",
"answer_explanat... | |
geo5k_00017 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, ∠AOB = 100°, then ∠A + ∠B equals ()\nChoices:\nA. 100°\nB. 80°\nC. 50°\nD. 40°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 17,
"answer": "C",
"question": "As shown in the figure, ∠AOB = 100°, then ∠A + ∠B equals ()",
"question_type": "mcq",
"pid": "25",
"choices": [
"100°",
"80°",
"50°",
"40°"
],
"correct_open": "50°",
"answer_explanation": "连接CO并延长交圆于点D由图可得∠由图可得∠A+∠B=\\frac{... | |
geo5k_00018 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, when planting trees on flat ground, the spacing between trees (the horizontal distance between two adjacent trees) is required to be 4m. If trees are planted on a slope with a gradient of 0.75, and the spacing is also required to be 4m, then the s... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 18,
"answer": "A",
"question": "As shown in the figure, when planting trees on flat ground, the spacing between trees (the horizontal distance between two adjacent trees) is required to be 4m. If trees are planted on a slope with a gradient of 0.75, and the spacing is also required ... | |
geo5k_00019 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, △ABC is inscribed in circle ⊙O, and AD is the diameter of ⊙O. If ∠ABC = 25°, what is the measure of ∠CAD?\nChoices:\nA. 25°\nB. 50°\nC. 65°\nD. 75°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 19,
"answer": "C",
"question": "As shown in the figure, △ABC is inscribed in circle ⊙O, and AD is the diameter of ⊙O. If ∠ABC = 25°, what is the measure of ∠CAD?",
"question_type": "mcq",
"pid": "27",
"choices": [
"25°",
"50°",
"65°",
"75°"
],
"correct_open... | |
geo5k_00020 | geo5k | [
{
"role": "user",
"content": "<image>Fold a strip of paper with parallel edges as shown in the figure. If ∠1 = 62°, then ∠2 equals ()\nChoices:\nA. 62°\nB. 56°\nC. 45°\nD. 30°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 20,
"answer": "B",
"question": "Fold a strip of paper with parallel edges as shown in the figure. If ∠1 = 62°, then ∠2 equals ()",
"question_type": "mcq",
"pid": "29",
"choices": [
"62°",
"56°",
"45°",
"30°"
],
"correct_open": "56°",
"answer_explanation":... | |
geo5k_00021 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, line a ∥ b, point B is on line b, and AB ⊥ BC, ∠2 = 65°, then the degree of ∠1 is ()\nChoices:\nA. 65°\nB. 25°\nC. 35°\nD. 45°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 21,
"answer": "B",
"question": "As shown in the figure, line a ∥ b, point B is on line b, and AB ⊥ BC, ∠2 = 65°, then the degree of ∠1 is () Choices: A. 65° B. 25° C. 35° D. 45°",
"question_type": "mcq",
"pid": "30",
"choices": [
"65°",
"25°",
"35°",
"45°"
],... | |
geo5k_00022 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, D is the midpoint of side AB. The triangle △ABC is folded along the line passing through D, so that point A falls on point F on BC. If ∠B = 50°, what is the degree of ∠EDF?\nChoices:\nA. 50°\nB. 40°\nC. 80°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 22,
"answer": "A",
"question": "As shown in the figure, D is the midpoint of side AB. The triangle △ABC is folded along the line passing through D, so that point A falls on point F on BC. If ∠B = 50°, what is the degree of ∠EDF?",
"question_type": "mcq",
"pid": "32",
"choices"... | |
geo5k_00023 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠CAB = 70°, △ABC is rotated counterclockwise around point A to the position of △AB′C′, such that CC′ ∥ AB. What is the degree of ∠BAB′?\nChoices:\nA. 70°\nB. 35°\nC. 40°\nD. 50°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 23,
"answer": "C",
"question": "As shown in the figure, in △ABC, ∠CAB = 70°, △ABC is rotated counterclockwise around point A to the position of △AB′C′, such that CC′ ∥ AB. What is the degree of ∠BAB′?",
"question_type": "mcq",
"pid": "35",
"choices": [
"70°",
"35°",
... | |
geo5k_00024 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, AB=AC, ∠A=36°, BD is the altitude on side AC. What is the measure of ∠DBC?\nChoices:\nA. 18°\nB. 24°\nC. 30°\nD. 36°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 24,
"answer": "A",
"question": "As shown in the figure, in △ABC, AB=AC, ∠A=36°, BD is the altitude on side AC. What is the measure of ∠DBC?",
"question_type": "mcq",
"pid": "37",
"choices": [
"18°",
"24°",
"30°",
"36°"
],
"correct_open": "18°",
"answer_ex... | |
geo5k_00025 | geo5k | [
{
"role": "user",
"content": "<image>Shaoxing is famous for its bridges. As shown in the figure, the distance from the top of the stone arch bridge to the water surface, CD, is 8m. The radius of the arch, OC, is 5m. What is the width of the water surface, AB?\nChoices:\nA. 4m\nB. 5m\nC. 6m\nD. 8m"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 25,
"answer": "D",
"question": "Shaoxing is famous for its bridges. As shown in the figure, the distance from the top of the stone arch bridge to the water surface, CD, is 8m. The radius of the arch, OC, is 5m. What is the width of the water surface, AB?",
"question_type": "mcq",
... | |
geo5k_00026 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given that the central angle ∠BOC = 78°, what is the degree measure of the inscribed angle ∠BAC?\nChoices:\nA. 156°\nB. 78°\nC. 39°\nD. 12°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 26,
"answer": "C",
"question": "As shown in the figure, given that the central angle ∠BOC = 78°, what is the degree measure of the inscribed angle ∠BAC?",
"question_type": "mcq",
"pid": "39",
"choices": [
"156°",
"78°",
"39°",
"12°"
],
"correct_open": "39°"... | |
geo5k_00027 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is known that ⊙O is the circumcircle of △ABD, AB is the diameter of ⊙O, CD is a chord of ⊙O, and ∠ABD = 58°. Then ∠BCD equals ()\nChoices:\nA. 116°\nB. 32°\nC. 58°\nD. 64°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 27,
"answer": "B",
"question": "As shown in the figure, it is known that ⊙O is the circumcircle of △ABD, AB is the diameter of ⊙O, CD is a chord of ⊙O, and ∠ABD = 58°. Then ∠BCD equals () Choices: A. 116° B. 32° C. 58° D. 64°",
"question_type": "mcq",
"pid": "40",
"choices": [... | |
geo5k_00028 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is known that E is a point on side BC of rhombus ABCD, and ∠DAE = ∠B = 80°. What is the degree measure of ∠CDE?\nChoices:\nA. 20°\nB. 25°\nC. 30°\nD. 35°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 28,
"answer": "C",
"question": "As shown in the figure, it is known that E is a point on side BC of rhombus ABCD, and ∠DAE = ∠B = 80°. What is the degree measure of ∠CDE?",
"question_type": "mcq",
"pid": "42",
"choices": [
"20°",
"25°",
"30°",
"35°"
],
"cor... | |
geo5k_00029 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, place the right-angle vertex of a set square containing a 30° angle on one of two parallel lines. If ∠1 = 35°, then the degree of ∠2 is ()\nChoices:\nA. 10°\nB. 20°\nC. 25°\nD. 30°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 29,
"answer": "C",
"question": "As shown in the figure, place the right-angle vertex of a set square containing a 30° angle on one of two parallel lines. If ∠1 = 35°, then the degree of ∠2 is () Choices: A. 10° B. 20° C. 25° D. 30°",
"question_type": "mcq",
"pid": "43",
"choic... | |
geo5k_00030 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in circle O, it is known that ∠OAB = 22.5°, then the degree of ∠C is ()\nChoices:\nA. 135°\nB. 122.5°\nC. 115.5°\nD. 112.5°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 30,
"answer": "D",
"question": "As shown in the figure, in circle O, it is known that ∠OAB = 22.5°, then the degree of ∠C is () Choices: A. 135° B. 122.5° C. 115.5° D. 112.5°",
"question_type": "mcq",
"pid": "44",
"choices": [
"135°",
"122.5°",
"115.5°",
"112.5... | |
geo5k_00031 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠ABC=45°, AC=8cm, F is the intersection point of altitudes AD and BE, then the length of BF is ()\nChoices:\nA. 4cm\nB. 6cm\nC. 8cm\nD. 9cm"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 31,
"answer": "C",
"question": "As shown in the figure, in △ABC, ∠ABC=45°, AC=8cm, F is the intersection point of altitudes AD and BE, then the length of BF is ()",
"question_type": "mcq",
"pid": "45",
"choices": [
"4cm",
"6cm",
"8cm",
"9cm"
],
"correct_ope... | |
geo5k_00032 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, AB=AC, ∠B=70°, then the measure of ∠A is ()\nChoices:\nA. 70°\nB. 55°\nC. 50°\nD. 40°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 32,
"answer": "D",
"question": "As shown in the figure, in △ABC, AB=AC, ∠B=70°, then the measure of ∠A is ()\nChoices:\nA. 70°\nB. 55°\nC. 50°\nD. 40°",
"question_type": "mcq",
"pid": "46",
"choices": [
"70°",
"55°",
"50°",
"40°"
],
"correct_open": "40°",
... | |
geo5k_00033 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, line a ∥ b, line c intersects a and b, ∠1 = 55°, then ∠2 = ()\nChoices:\nA. 55°\nB. 35°\nC. 125°\nD. 65°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 33,
"answer": "A",
"question": "As shown in the figure, line a ∥ b, line c intersects a and b, ∠1 = 55°, then ∠2 = () Choices: A. 55° B. 35° C. 125° D. 65°",
"question_type": "mcq",
"pid": "48",
"choices": [
"55°",
"35°",
"125°",
"65°"
],
"correct_open": "5... | |
geo5k_00034 | geo5k | [
{
"role": "user",
"content": "<image>In the isosceles right triangle ABC, AB = AC = 4, point O is the midpoint of BC. With O as the center, draw circle ⊙O intersecting BC at points M and N. Circle ⊙O is tangent to AB and AC at points D and E, respectively. What are the radius of ⊙O and the degree measure of... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 34,
"answer": "A",
"question": "In the isosceles right triangle ABC, AB = AC = 4, point O is the midpoint of BC. With O as the center, draw circle ⊙O intersecting BC at points M and N. Circle ⊙O is tangent to AB and AC at points D and E, respectively. What are the radius of ⊙O and t... | |
geo5k_00035 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the diameter CD of circle O passes through the midpoint G of chord EF, and ∠DCF = 20°. Then ∠EOD is equal to ()\nChoices:\nA. 10°\nB. 20°\nC. 40°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 35,
"answer": "C",
"question": "As shown in the figure, the diameter CD of circle O passes through the midpoint G of chord EF, and ∠DCF = 20°. Then ∠EOD is equal to ()",
"question_type": "mcq",
"pid": "50",
"choices": [
"10°",
"20°",
"40°",
"80°"
],
"correc... | |
geo5k_00036 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB is parallel to CD. If ∠B = 20°, then ∠C is ()\nChoices:\nA. 40°\nB. 20°\nC. 60°\nD. 70°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 36,
"answer": "B",
"question": "As shown in the figure, AB is parallel to CD. If ∠B = 20°, then ∠C is ()",
"question_type": "mcq",
"pid": "51",
"choices": [
"40°",
"20°",
"60°",
"70°"
],
"correct_open": "20°",
"answer_explanation": "∵AB//CD,,∠B=20^{°}∴∠C=... | |
geo5k_00037 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, ∠1 = 100°, ∠C = 70°, then the measure of ∠A is ()\nChoices:\nA. 10°\nB. 20°\nC. 30°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 37,
"answer": "C",
"question": "As shown in the figure, ∠1 = 100°, ∠C = 70°, then the measure of ∠A is ()",
"question_type": "mcq",
"pid": "52",
"choices": [
"10°",
"20°",
"30°",
"80°"
],
"correct_open": "30°",
"answer_explanation": "根据三角形的一个外角等于与它不相邻的两个内... | |
geo5k_00038 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in circle ⊙O, ∠ABC = 50°, then ∠AOC is equal to ()\nChoices:\nA. 50°\nB. 80°\nC. 90°\nD. 100°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 38,
"answer": "D",
"question": "As shown in the figure, in circle ⊙O, ∠ABC = 50°, then ∠AOC is equal to ()\nChoices:\nA. 50°\nB. 80°\nC. 90°\nD. 100°",
"question_type": "mcq",
"pid": "53",
"choices": [
"50°",
"80°",
"90°",
"100°"
],
"correct_open": "100°",
... | |
geo5k_00039 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, two right-angled triangles with angles of 30° and 45° respectively are combined to form the following shape, where ∠C=90°, ∠B=45°, ∠E=30°. What is the degree measure of ∠BFD?\nChoices:\nA. 15°\nB. 25°\nC. 30°\nD. 10°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 39,
"answer": "A",
"question": "As shown in the figure, two right-angled triangles with angles of 30° and 45° respectively are combined to form the following shape, where ∠C=90°, ∠B=45°, ∠E=30°. What is the degree measure of ∠BFD?",
"question_type": "mcq",
"pid": "54",
"choice... | |
geo5k_00040 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is known that AB∥CD, E is a point on AB, and ED bisects ∠BEC, intersecting CD at point D. If ∠BEC=100°, then the degree of ∠D is ()\nChoices:\nA. 50°\nB. 100°\nC. 80°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 40,
"answer": "D",
"question": "As shown in the figure, it is known that AB∥CD, E is a point on AB, and ED bisects ∠BEC, intersecting CD at point D. If ∠BEC=100°, then the degree of ∠D is () Choices: A. 50° B. 100° C. 80° D. 60°",
"question_type": "mcq",
"pid": "55",
"choices"... | |
geo5k_00041 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, ∠CED=90°, ∠AEC=35°, then the measure of ∠D is ()\nChoices:\nA. 65°\nB. 55°\nC. 45°\nD. 35°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 41,
"answer": "B",
"question": "As shown in the figure, AB∥CD, ∠CED=90°, ∠AEC=35°, then the measure of ∠D is ()",
"question_type": "mcq",
"pid": "56",
"choices": [
"65°",
"55°",
"45°",
"35°"
],
"correct_open": "55°",
"answer_explanation": "∵AB//CD,∴∠D=∠BE... | |
geo5k_00042 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, AD bisects ∠BAC, and ∠C=80°, then the measure of ∠D is ()\nChoices:\nA. 50°\nB. 60°\nC. 70°\nD. 100°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 42,
"answer": "A",
"question": "As shown in the figure, AB∥CD, AD bisects ∠BAC, and ∠C=80°, then the measure of ∠D is () Choices: A. 50° B. 60° C. 70° D. 100°",
"question_type": "mcq",
"pid": "57",
"choices": [
"50°",
"60°",
"70°",
"100°"
],
"correct_open":... | |
geo5k_00043 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, AD bisects ∠BAC. If ∠BAD=70°, then the measure of ∠ACD is ()\nChoices:\nA. 40°\nB. 35°\nC. 50°\nD. 45°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 43,
"answer": "A",
"question": "As shown in the figure, AB∥CD, AD bisects ∠BAC. If ∠BAD=70°, then the measure of ∠ACD is () Choices: A. 40° B. 35° C. 50° D. 45°",
"question_type": "mcq",
"pid": "58",
"choices": [
"40°",
"35°",
"50°",
"45°"
],
"correct_open"... | |
geo5k_00044 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given AB∥CD, ∠2=135°, what is the degree of ∠1?\nChoices:\nA. 35°\nB. 45°\nC. 55°\nD. 65°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 44,
"answer": "B",
"question": "As shown in the figure, given AB∥CD, ∠2=135°, what is the degree of ∠1?",
"question_type": "mcq",
"pid": "59",
"choices": [
"35°",
"45°",
"55°",
"65°"
],
"correct_open": "45°",
"answer_explanation": "试题分析:∵AB//CD,∴∠1=∠3,∵∠2... | |
geo5k_00045 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, points A, B, and C are on circle ⊙O. If ∠OBC = 50°, then the degree measure of ∠A is ()\nChoices:\nA. 40°\nB. 50°\nC. 80°\nD. 100°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 45,
"answer": "A",
"question": "As shown in the figure, points A, B, and C are on circle ⊙O. If ∠OBC = 50°, then the degree measure of ∠A is ()",
"question_type": "mcq",
"pid": "60",
"choices": [
"40°",
"50°",
"80°",
"100°"
],
"correct_open": "40°",
"answ... | |
geo5k_00046 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, place two vertices of a right triangle containing a 45° angle on the opposite edges of a ruler. If ∠1 = 20°, then the degree of ∠2 is ()\nChoices:\nA. 15°\nB. 20°\nC. 25°\nD. 30°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 46,
"answer": "C",
"question": "As shown in the figure, place two vertices of a right triangle containing a 45° angle on the opposite edges of a ruler. If ∠1 = 20°, then the degree of ∠2 is ()",
"question_type": "mcq",
"pid": "61",
"choices": [
"15°",
"20°",
"25°",... | |
geo5k_00047 | geo5k | [
{
"role": "user",
"content": "<image>Place a ruler and a set square as shown in the figure. If ∠1 = 40°, then the measure of ∠2 is ()\nChoices:\nA. 125°\nB. 120°\nC. 140°\nD. 130°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 47,
"answer": "D",
"question": "Place a ruler and a set square as shown in the figure. If ∠1 = 40°, then the measure of ∠2 is ()",
"question_type": "mcq",
"pid": "63",
"choices": [
"125°",
"120°",
"140°",
"130°"
],
"correct_open": "130°",
"answer_explanat... | |
geo5k_00048 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠C=90°, AC=4 cm, AB=7 cm, AD bisects ∠BAC and intersects BC at D, DE⊥AB at E, then the length of EB is ()\nChoices:\nA. 3㎝\nB. 4㎝\nC. 5㎝\nD. 不能确定"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 48,
"answer": "A",
"question": "As shown in the figure, in △ABC, ∠C=90°, AC=4 cm, AB=7 cm, AD bisects ∠BAC and intersects BC at D, DE⊥AB at E, then the length of EB is ()",
"question_type": "mcq",
"pid": "64",
"choices": [
"3㎝",
"4㎝",
"5㎝",
"不能确定"
],
"corre... | |
geo5k_00049 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, A, C, and B are three points on circle ⊙O. If ∠AOC = 40°, then the measure of ∠ABC is ().\nChoices:\nA. 10°\nB. 20°\nC. 40°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 49,
"answer": "B",
"question": "As shown in the figure, A, C, and B are three points on circle ⊙O. If ∠AOC = 40°, then the measure of ∠ABC is (). Choices: A. 10° B. 20° C. 40° D. 80°",
"question_type": "mcq",
"pid": "65",
"choices": [
"10°",
"20°",
"40°",
"80°"... | |
geo5k_00050 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠ABO = 30°, what is the measure of ∠ACB?\nChoices:\nA. 30°\nB. 45°\nC. 50°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 50,
"answer": "D",
"question": "As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠ABO = 30°, what is the measure of ∠ACB?",
"question_type": "mcq",
"pid": "66",
"choices": [
"30°",
"45°",
"50°",
"60°"
],
"correct_open": "60°",
"answer_ex... | |
geo5k_00051 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠BAC = 50°, then ∠ADC is ()\nChoices:\nA. 40°\nB. 50°\nC. 80°\nD. 100°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 51,
"answer": "A",
"question": "As shown in the figure, AB is the diameter of circle O, and points C and D are on circle O. If ∠BAC = 50°, then ∠ADC is ()\nChoices:\nA. 40°\nB. 50°\nC. 80°\nD. 100°",
"question_type": "mcq",
"pid": "69",
"choices": [
"40°",
"50°",
"... | |
geo5k_00052 | geo5k | [
{
"role": "user",
"content": "<image>Given that in the figure, △OAD ≌ △OBC, and ∠O = 70°, ∠C = 25°, then ∠OAD = ()\nChoices:\nA. 95°\nB. 85°\nC. 75°\nD. 65°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 52,
"answer": "B",
"question": "Given that in the figure, △OAD ≌ △OBC, and ∠O = 70°, ∠C = 25°, then ∠OAD = () Choices: A. 95° B. 85° C. 75° D. 65°",
"question_type": "mcq",
"pid": "70",
"choices": [
"95°",
"85°",
"75°",
"65°"
],
"correct_open": "85°",
"an... | |
geo5k_00053 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, ⊙O is the circumcircle of △ABC. If ∠ABC = 40°, then the measure of ∠AOC is ()\nChoices:\nA. 20°\nB. 40°\nC. 60°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 53,
"answer": "D",
"question": "As shown in the figure, ⊙O is the circumcircle of △ABC. If ∠ABC = 40°, then the measure of ∠AOC is ()",
"question_type": "mcq",
"pid": "72",
"choices": [
"20°",
"40°",
"60°",
"80°"
],
"correct_open": "80°",
"answer_explanat... | |
geo5k_00054 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, BO and CO bisect ∠ABC and ∠ACB respectively, and MN∥BC. If AB=36 and AC=24, what is the perimeter of △AMN?\nChoices:\nA. 60\nB. 66\nC. 72\nD. 78"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 54,
"answer": "A",
"question": "As shown in the figure, BO and CO bisect ∠ABC and ∠ACB respectively, and MN∥BC. If AB=36 and AC=24, what is the perimeter of △AMN?",
"question_type": "mcq",
"pid": "75",
"choices": [
"60",
"66",
"72",
"78"
],
"correct_open": ... | |
geo5k_00055 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, a∥b, ∠1=130°, then the degree of ∠2 is equal to ()\nChoices:\nA. 50°\nB. 70°\nC. 120°\nD. 130°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 55,
"answer": "D",
"question": "As shown in the figure, a∥b, ∠1=130°, then the degree of ∠2 is equal to ()",
"question_type": "mcq",
"pid": "78",
"choices": [
"50°",
"70°",
"120°",
"130°"
],
"correct_open": "130°",
"answer_explanation": "∵allb(已知)∴∠3=∠1=1... | |
geo5k_00056 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠C=90°, point D is on side AC, and DE∥AB. If ∠ADE=46°, then the measure of ∠B is ()\nChoices:\nA. 34°\nB. 44°\nC. 46°\nD. 54°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 56,
"answer": "B",
"question": "As shown in the figure, in △ABC, ∠C=90°, point D is on side AC, and DE∥AB. If ∠ADE=46°, then the measure of ∠B is () Choices: A. 34° B. 44° C. 46° D. 54°",
"question_type": "mcq",
"pid": "79",
"choices": [
"34°",
"44°",
"46°",
"5... | |
geo5k_00057 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is measured that BD = \"120\" m, DC = \"60\" m, EC = \"50\" m. What is the width of the river AB?\nChoices:\nA. 120m\nB. 100m\nC. 75m\nD. 25m"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 57,
"answer": "B",
"question": "As shown in the figure, it is measured that BD = \"120\" m, DC = \"60\" m, EC = \"50\" m. What is the width of the river AB? Choices: A. 120m B. 100m C. 75m D. 25m",
"question_type": "mcq",
"pid": "80",
"choices": [
"120m",
"100m",
"... | |
geo5k_00058 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, point E is on BC, and CD=CE, ∠D=74°, then the measure of ∠B is ()\nChoices:\nA. 74°\nB. 32°\nC. 22°\nD. 16°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 58,
"answer": "B",
"question": "As shown in the figure, AB∥CD, point E is on BC, and CD=CE, ∠D=74°, then the measure of ∠B is ()",
"question_type": "mcq",
"pid": "81",
"choices": [
"74°",
"32°",
"22°",
"16°"
],
"correct_open": "32°",
"answer_explanation":... | |
geo5k_00059 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠A=90°, point D is on side AC, and DE∥BC. If ∠1=145°, then the measure of ∠B is ()\nChoices:\nA. 35°\nB. 25°\nC. 45°\nD. 55°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 59,
"answer": "D",
"question": "As shown in the figure, in △ABC, ∠A=90°, point D is on side AC, and DE∥BC. If ∠1=145°, then the measure of ∠B is ()",
"question_type": "mcq",
"pid": "82",
"choices": [
"35°",
"25°",
"45°",
"55°"
],
"correct_open": "55°",
"a... | |
geo5k_00060 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, BC∥DE, if ∠B=40°, then the degree of ∠D is ()\nChoices:\nA. 40°\nB. 140°\nC. 160°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 60,
"answer": "B",
"question": "As shown in the figure, AB∥CD, BC∥DE, if ∠B=40°, then the degree of ∠D is ()",
"question_type": "mcq",
"pid": "83",
"choices": [
"40°",
"140°",
"160°",
"60°"
],
"correct_open": "140°",
"answer_explanation": "试题解析:∵AB//CD,∠B... | |
geo5k_00061 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the three vertices of △ABC are on lines a and b, respectively, and a∥b. If ∠1=120° and ∠2=80°, then the measure of ∠3 is ()\nChoices:\nA. 40°\nB. 60°\nC. 80°\nD. 120°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 61,
"answer": "A",
"question": "As shown in the figure, the three vertices of △ABC are on lines a and b, respectively, and a∥b. If ∠1=120° and ∠2=80°, then the measure of ∠3 is ()\nChoices:\nA. 40°\nB. 60°\nC. 80°\nD. 120°",
"question_type": "mcq",
"pid": "84",
"choices": [
... | |
geo5k_00062 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, point E is on the extension of CA. If ∠BAE=40°, then the measure of ∠ACD is ()\nChoices:\nA. 150°\nB. 140°\nC. 130°\nD. 120°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 62,
"answer": "B",
"question": "As shown in the figure, AB∥CD, point E is on the extension of CA. If ∠BAE=40°, then the measure of ∠ACD is ()\nChoices:\nA. 150°\nB. 140°\nC. 130°\nD. 120°",
"question_type": "mcq",
"pid": "86",
"choices": [
"150°",
"140°",
"130°",
... | |
geo5k_00063 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB ∥ CD, AF intersects CD at point O, and OF bisects ∠EOD. If ∠A = 34°, then the degree of ∠EOD is ()\nChoices:\nA. 34°\nB. 68°\nC. 102°\nD. 146°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 63,
"answer": "B",
"question": "As shown in the figure, AB ∥ CD, AF intersects CD at point O, and OF bisects ∠EOD. If ∠A = 34°, then the degree of ∠EOD is () Choices: A. 34° B. 68° C. 102° D. 146°",
"question_type": "mcq",
"pid": "87",
"choices": [
"34°",
"68°",
"1... | |
geo5k_00064 | geo5k | [
{
"role": "user",
"content": "<image>In a certain activity class, two study groups, Group A and Group B, measured some objects on the campus under the sunlight at the same time. Below is some information they obtained through measurement: As shown in Figure 1, Group A measured the shadow length of a bamboo ... | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 64,
"answer": "D",
"question": "In a certain activity class, two study groups, Group A and Group B, measured some objects on the campus under the sunlight at the same time. Below is some information they obtained through measurement: As shown in Figure 1, Group A measured the shadow... | |
geo5k_00065 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, quadrilateral ABCD is a cyclic quadrilateral inscribed in circle O. If ∠BCD = 110°, then the measure of ∠BAD is ()\nChoices:\nA. 140°\nB. 110°\nC. 90°\nD. 70°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 65,
"answer": "D",
"question": "As shown in the figure, quadrilateral ABCD is a cyclic quadrilateral inscribed in circle O. If ∠BCD = 110°, then the measure of ∠BAD is ()",
"question_type": "mcq",
"pid": "89",
"choices": [
"140°",
"110°",
"90°",
"70°"
],
"c... | |
geo5k_00066 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is known that AB∥CD and EA is the bisector of ∠CEB. If ∠BED=40°, then the degree of ∠A is ()\nChoices:\nA. 40°\nB. 50°\nC. 70°\nD. 80°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 66,
"answer": "C",
"question": "As shown in the figure, it is known that AB∥CD and EA is the bisector of ∠CEB. If ∠BED=40°, then the degree of ∠A is () Choices: A. 40° B. 50° C. 70° D. 80°",
"question_type": "mcq",
"pid": "90",
"choices": [
"40°",
"50°",
"70°",
... | |
geo5k_00067 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, Xiaocong places two vertices of a right triangle with a 60° angle on the opposite sides of a ruler and measures ∠1 = 23°. What is the degree of ∠2?\nChoices:\nA. 23°\nB. 22°\nC. 37°\nD. 67°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 67,
"answer": "C",
"question": "As shown in the figure, Xiaocong places two vertices of a right triangle with a 60° angle on the opposite sides of a ruler and measures ∠1 = 23°. What is the degree of ∠2?",
"question_type": "mcq",
"pid": "91",
"choices": [
"23°",
"22°",... | |
geo5k_00068 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB = AC, AD ∥ BC, ∠BAC = 100°, then the degree of ∠CAD is ()\nChoices:\nA. 30°\nB. 35°\nC. 40°\nD. 50°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 68,
"answer": "C",
"question": "As shown in the figure, AB = AC, AD ∥ BC, ∠BAC = 100°, then the degree of ∠CAD is ()",
"question_type": "mcq",
"pid": "92",
"choices": [
"30°",
"35°",
"40°",
"50°"
],
"correct_open": "40°",
"answer_explanation": "试题分析:根据等腰三... | |
geo5k_00069 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB∥CD, and point E is on the extension of CB. If ∠ABE=70°, then the degree of ∠ECD is ()\nChoices:\nA. 20°\nB. 70°\nC. 100°\nD. 110°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 69,
"answer": "D",
"question": "As shown in the figure, AB∥CD, and point E is on the extension of CB. If ∠ABE=70°, then the degree of ∠ECD is ()",
"question_type": "mcq",
"pid": "93",
"choices": [
"20°",
"70°",
"100°",
"110°"
],
"correct_open": "110°",
"a... | |
geo5k_00070 | geo5k | [
{
"role": "user",
"content": "<image>In a cylindrical oil tank with a diameter of 200 cm, some oil is filled, and the cross-section is as shown in the figure. If the width of the oil surface AB = 160 cm, what is the maximum depth of the oil?\nChoices:\nA. 40cm\nB. 60cm\nC. 80cm\nD. 100cm"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 70,
"answer": "A",
"question": "In a cylindrical oil tank with a diameter of 200 cm, some oil is filled, and the cross-section is as shown in the figure. If the width of the oil surface AB = 160 cm, what is the maximum depth of the oil? Choices: A. 40 cm B. 60 cm C. 80 cm D. 100 cm"... | |
geo5k_00071 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, place the right angle vertex of an isosceles right triangle on one edge of a ruler. If ∠1 = 40°, then ∠2 = ()\nChoices:\nA. 40°\nB. 45°\nC. 50°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 71,
"answer": "C",
"question": "As shown in the figure, place the right angle vertex of an isosceles right triangle on one edge of a ruler. If ∠1 = 40°, then ∠2 = () Choices: A. 40° B. 45° C. 50° D. 60°",
"question_type": "mcq",
"pid": "96",
"choices": [
"40°",
"45°",
... | |
geo5k_00072 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, when a road is built to the lakeside, it needs to turn around the lake. If the first turning angle ∠A is 120°, the second turning angle ∠B is 150°, and the third turning angle is ∠C, at this point the road is exactly parallel to the road before th... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 72,
"answer": "A",
"question": "As shown in the figure, when a road is built to the lakeside, it needs to turn around the lake. If the first turning angle ∠A is 120°, the second turning angle ∠B is 150°, and the third turning angle is ∠C, at this point the road is exactly parallel t... | |
geo5k_00073 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the slant height of the conical mold is 10 cm, and the radius of the base is 5 cm. What is the lateral surface area of this conical mold?\nChoices:\nA. 10πcm\nB. 50πcm\nC. 100πcm\nD. 150πcm"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 73,
"answer": "B",
"question": "As shown in the figure, the slant height of the conical mold is 10 cm, and the radius of the base is 5 cm. What is the lateral surface area of this conical mold?",
"question_type": "mcq",
"pid": "98",
"choices": [
"10πcm",
"50πcm",
"... | |
geo5k_00074 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, the points A and C to be measured are separated by a pond. Master Li randomly selects a point B outside of AC, connects BA and BC, and takes the midpoints E and F of BA and BC, respectively. It is measured that the distance between points E and F ... | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 74,
"answer": "A",
"question": "As shown in the figure, the points A and C to be measured are separated by a pond. Master Li randomly selects a point B outside of AC, connects BA and BC, and takes the midpoints E and F of BA and BC, respectively. It is measured that the distance bet... | |
geo5k_00075 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, point D is on BC, AB=AD=DC, ∠B=80°, then the measure of ∠C is ()\nChoices:\nA. 30°\nB. 40°\nC. 45°\nD. 60°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 75,
"answer": "B",
"question": "As shown in the figure, in △ABC, point D is on BC, AB=AD=DC, ∠B=80°, then the measure of ∠C is () Choices: A. 30° B. 40° C. 45° D. 60°",
"question_type": "mcq",
"pid": "100",
"choices": [
"30°",
"40°",
"45°",
"60°"
],
"correc... | |
geo5k_00076 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, BD bisects ∠ABC, and CD∥AB. If ∠BCD=70°, then the measure of ∠CDB is ()\nChoices:\nA. 55°\nB. 50°\nC. 45°\nD. 30°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 76,
"answer": "A",
"question": "As shown in the figure, BD bisects ∠ABC, and CD∥AB. If ∠BCD=70°, then the measure of ∠CDB is () Choices: A. 55° B. 50° C. 45° D. 30°",
"question_type": "mcq",
"pid": "101",
"choices": [
"55°",
"50°",
"45°",
"30°"
],
"correct_... | |
geo5k_00077 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, it is known that AB∥CD, AD bisects ∠BAE, and ∠D=38°. What is the degree measure of ∠AEC?\nChoices:\nA. 19°\nB. 38°\nC. 72°\nD. 76°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 77,
"answer": "D",
"question": "As shown in the figure, it is known that AB∥CD, AD bisects ∠BAE, and ∠D=38°. What is the degree measure of ∠AEC?",
"question_type": "mcq",
"pid": "102",
"choices": [
"19°",
"38°",
"72°",
"76°"
],
"correct_open": "76°",
"ans... | |
geo5k_00078 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, AB is tangent to circle O at point B, and the extension of AO intersects circle O at point C. Connect BC. If ∠A = 36°, then ∠C equals ()\nChoices:\nA. 36°\nB. 54°\nC. 60°\nD. 27°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 78,
"answer": "D",
"question": "As shown in the figure, AB is tangent to circle O at point B, and the extension of AO intersects circle O at point C. Connect BC. If ∠A = 36°, then ∠C equals () Choices: A. 36° B. 54° C. 60° D. 27°",
"question_type": "mcq",
"pid": "103",
"choice... | |
geo5k_00079 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in the cyclic quadrilateral ABCD, if ∠C = 80°, then ∠A equals ()\nChoices:\nA. 120°\nB. 100°\nC. 80°\nD. 90°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 79,
"answer": "B",
"question": "As shown in the figure, in the cyclic quadrilateral ABCD, if ∠C = 80°, then ∠A equals ()",
"question_type": "mcq",
"pid": "104",
"choices": [
"120°",
"100°",
"80°",
"90°"
],
"correct_open": "100°",
"answer_explanation": "试题... | |
geo5k_00080 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, in △ABC, ∠ABC=50°, ∠ACB=80°, BP bisects ∠ABC, CP bisects ∠ACB, then the measure of ∠BPC is ()\nChoices:\nA. 100°\nB. 110°\nC. 115°\nD. 120°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 80,
"answer": "C",
"question": "As shown in the figure, in △ABC, ∠ABC=50°, ∠ACB=80°, BP bisects ∠ABC, CP bisects ∠ACB, then the measure of ∠BPC is () Choices: A. 100° B. 110° C. 115° D. 120°",
"question_type": "mcq",
"pid": "105",
"choices": [
"100°",
"110°",
"115°... | |
geo5k_00081 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, place the right-angle vertex of the triangle on one edge of the ruler. If ∠1 = 65°, then the degree of ∠2 is ()\nChoices:\nA. 10°\nB. 15°\nC. 20°\nD. 25°"
}
] | math | {
"style": "rule",
"ground_truth": "D"
} | {
"split": "train",
"index": 81,
"answer": "D",
"question": "As shown in the figure, place the right-angle vertex of the triangle on one edge of the ruler. If ∠1 = 65°, then the degree of ∠2 is ()",
"question_type": "mcq",
"pid": "106",
"choices": [
"10°",
"15°",
"20°",
"25°"
],
"corre... | |
geo5k_00082 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, given AB∥CD, ∠1=56°, what is the degree of ∠2?\nChoices:\nA. 34°\nB. 56°\nC. 65°\nD. 124°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 82,
"answer": "B",
"question": "As shown in the figure, given AB∥CD, ∠1=56°, what is the degree of ∠2?",
"question_type": "mcq",
"pid": "107",
"choices": [
"34°",
"56°",
"65°",
"124°"
],
"correct_open": "56°",
"answer_explanation": "因为AB//CD,所以∠1=∠2,又∠1=5... | |
geo5k_00083 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, BC is the diameter of circle O, and AD is perpendicular to BC. If ∠D = 36°, then the measure of ∠BAD is ()\nChoices:\nA. 72°\nB. 54°\nC. 45°\nD. 36°"
}
] | math | {
"style": "rule",
"ground_truth": "B"
} | {
"split": "train",
"index": 83,
"answer": "B",
"question": "As shown in the figure, BC is the diameter of circle O, and AD is perpendicular to BC. If ∠D = 36°, then the measure of ∠BAD is ()",
"question_type": "mcq",
"pid": "108",
"choices": [
"72°",
"54°",
"45°",
"36°"
],
"correct_op... | |
geo5k_00084 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, line AB is parallel to line CD. If ∠1 = 70°, then the degree of ∠BOF is ()\nChoices:\nA. 70°\nB. 100°\nC. 110°\nD. 120°"
}
] | math | {
"style": "rule",
"ground_truth": "C"
} | {
"split": "train",
"index": 84,
"answer": "C",
"question": "As shown in the figure, line AB is parallel to line CD. If ∠1 = 70°, then the degree of ∠BOF is ()\nChoices:\nA. 70°\nB. 100°\nC. 110°\nD. 120°",
"question_type": "mcq",
"pid": "109",
"choices": [
"70°",
"100°",
"110°",
"120°"
... | |
geo5k_00085 | geo5k | [
{
"role": "user",
"content": "<image>As shown in the figure, lines a and b intersect at point O. If ∠1 is equal to 50°, then ∠2 is equal to ()\nChoices:\nA. 50°\nB. 40°\nC. 140°\nD. 130°"
}
] | math | {
"style": "rule",
"ground_truth": "A"
} | {
"split": "train",
"index": 85,
"answer": "A",
"question": "As shown in the figure, lines a and b intersect at point O. If ∠1 is equal to 50°, then ∠2 is equal to () Choices: A. 50° B. 40° C. 140° D. 130°",
"question_type": "mcq",
"pid": "110",
"choices": [
"50°",
"40°",
"140°",
"130°"
... |
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