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<image>Find x. Round to the nearest tenth, if necessary.
11
1,106
[ "8", "9", "10", "11" ]
D
<image>In the figure, the vertices of quadrilateral ABCD intersect square EFGH and divide its sides into segments with measures that have a ratio of 1:2. Find the ratio between the areas of ABCD and EFGH.
5:9
1,354
[ "1:4", "1:2", "5:9", "1: \\sqrt 2" ]
C
<image>Find the value of $f$ in the parallelogram
14
704
[ "14", "18", "36", "56" ]
A
<image>Find the value of the variable $y$ in the figure.
125
468
[ "55", "115", "125", "135" ]
C
<image>Find $m\angle S$
123
1,005
[ "68", "80", "123", "125" ]
C
<image>Find $x$ so that $ m \parallel n $.
13
1,811
[ "10", "11", "12", "13" ]
D
<image>Find $ m ∠RSU $ so that $ m \parallel n $.
124
1,861
[ "114", "116", "120", "124" ]
D
<image>Find $x$.
12
1,676
[ "6", "9", "12", "15" ]
C
<image>Find the perimeter of the $\triangle A B C,$ if $\triangle A B C \sim \triangle C B D, A D=5$, $C D=12,$ and $B C=31.2$
78
68
[ "32.5", "72", "78", "187.2" ]
C
<image>$\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the diameter of the circle.
17
2,074
[ "8", "8.5", "15", "17" ]
D
<image>Find $\angle 10$
50
1,047
[ "50", "80", "100", "160" ]
A
<image>Find the measure of $\angle 7$ if $\overline{A B} \perp \overline{B C}$.
140
606
[ "110", "120", "130", "140" ]
D
<image>Find $m \widehat {CF}$.
80
973
[ "40", "49", "80", "98" ]
C
<image>$\overline{BC} \| \overline{DF}$. $AC=15$, $BD=3x-2$, $CF=3x+2$, and $AB=12$. Find $x$.
6
1,982
[ "3", "4", "5", "6" ]
D
<image>Each pair of polygons is similar. Find y
70
1,298
[ "70", "80", "100", "150" ]
A
<image>Find x.
12
1,548
[ "9", "12", "15", "16" ]
B
<image>Quadrilateral ABCD is a rectangle. If $m\angle ADB = 4x + 8$ and $m\angle DBA = 6x + 12$, find x.
7
1,023
[ "7", "20", "36", "54" ]
A
<image>Find $x$.
2
84
[ "1", "2", "3", "4" ]
B
<image>Find x
22
1,119
[ "22", "24", "43", "68" ]
A
<image>Find x. Assume that any segment that appears to be tangent is tangent.
13
1,873
[ "13", "34", "106", "160" ]
A
<image>Find the perimeter of quadrilateral ABCD.
40 + 14 \sqrt { 2 }
157
[ "27 + 14 \\sqrt { 2 }", "40 + 14 \\sqrt { 2 }", "27 + 28 \\sqrt { 2 }", "40 + 28 \\sqrt { 2 }" ]
B
<image>Find $EG$.
10
1,394
[ "5", "6.5", "10", "13" ]
C
<image>In $\triangle JLP$, $m \angle JMP=3 x-6$, $JK=3y-2$, and $LK=5y-8$. Find $LK$ if $\overline{PK}$ is a median.
7
1,286
[ "2", "5", "7", "8" ]
C
<image>Find $ST$.
5
1,435
[ "5", "10", "12", "16" ]
A
<image>Find the measure of the altitude drawn to the hypotenuse.
\sqrt { 612 }
850
[ "18", "\\sqrt { 612 }", "34", "612" ]
B
<image>Use parallelogram $ABCD$ to find $AB$
12
1,593
[ "6", "12", "18", "115" ]
B
<image>Find the area of the figure. Round to the nearest tenth if necessary.
39.4
1,663
[ "39.4", "49.0", "68.2", "78.7" ]
A
<image>Find $x$ if $\odot M \cong \odot N$.
9
1,100
[ "8", "9", "10", "12" ]
B
<image>Find x. Round side measures to the nearest tenth.
35.1
1,213
[ "16.4", "18.0", "32.0", "35.1" ]
D
<image>Find x.
2 \sqrt { 5 }
1,559
[ "2 \\sqrt { 2 }", "3 \\sqrt { 2 }", "2 \\sqrt { 5 }", "3 \\sqrt { 5 }" ]
C
<image>If $QT=11$, what is $QU$.
11
1,635
[ "7", "8", "11", "16" ]
C
<image>$a=14, b=48,$ and $c=50$ find $tanA$
0.29
273
[ "0.17", "0.19", "0.29", "0.50" ]
C
<image>Find $y$ so that the quadrilateral is a parallelogram
41
1,433
[ "9", "20", "21", "41" ]
D
<image>$\ln \odot K$, $ M N=16$ and $m \widehat{M N}=98$. Find the measure of $LN$. Round to the nearest hundredth.
8.94
8
[ "6.93", "7.50", "8.94", "10.00" ]
C
<image>In the figure, $QR \| TS$, $QT \| RS$, and $m \angle 1=131$. Find the measure of $\angle 6$.
131
1,045
[ "101", "111", "121", "131" ]
D
<image>Find the measure of $m∠C$.
70
2,017
[ "35", "70", "90", "140" ]
B
<image>Find x
7
1,533
[ "7", "9", "11", "15" ]
A
<image>Find $m \angle 2$.
39
1,763
[ "33", "39", "51", "108" ]
B
<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ
6
749
[ "5.5", "6", "8", "11" ]
B
<image>Find z.
12 \sqrt { 3 }
457
[ "6 \\sqrt { 3 }", "12 \\sqrt { 3 }", "18 \\sqrt { 2 }", "36" ]
B
<image>WXYZ is a parallelogram. Find $m \angle Y Z W$
115
49
[ "33", "65", "82", "115" ]
D
<image>Find $XZ$.
23
257
[ "5", "15", "23", "35" ]
C
<image>Find y.
10
347
[ "6", "8", "10", "12" ]
C
<image>Find the measure of $\angle 1$.
56
330
[ "56", "66", "76", "86" ]
A
<image>Find $x$.
60
45
[ "50", "55", "60", "70" ]
C
<image>Find the area of the figure.
150
744
[ "105", "135", "150", "160" ]
C
<image>In $\odot P, m \widehat{E N}=66$ and $m \angle G P M=89$ . Find $m \angle G N M$
44.5
454
[ "44.5", "66", "89", "155" ]
A
<image>Find $x$ so that the quadrilateral is a parallelogram
3
962
[ "3", "5", "7", "8" ]
A
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
1520
229
[ "1064", "1120", "1520", "1888.1" ]
C
<image>Find $x$.
3
585
[ "2", "3", "4", "5" ]
B
<image>Find $y$.
3
1,490
[ "1", "2", "3", "4" ]
C
<image>WXYZ is a parallelogram. Find $m \angle X W Z$
65
1,801
[ "33", "65", "82", "115" ]
B
<image>Find x.
\frac { 15 \sqrt { 2 } } { 2 }
1,669
[ "\\frac { 15 } { 2 }", "\\frac { 15 \\sqrt { 2 } } { 2 }", "\\frac { 15 \\sqrt { 3 } } { 2 }", "15 \\sqrt { 2 }" ]
B
<image>Find $x$ in the figure.
34
434
[ "27.7", "34", "41.3", "68" ]
B
<image>Find the measure of $\angle 1$ if $m \angle D G F=53$ and $m \angle A G C=40$.
37
52
[ "37", "40", "50", "53" ]
A
<image>Find the measure of the altitude drawn to the hypotenuse.
3 \sqrt { 5 }
680
[ "\\sqrt { 3 }", "\\sqrt { 5 }", "3", "3 \\sqrt { 5 }" ]
D
<image>Chords $\overline{JF}$ and $\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$
6
807
[ "6", "12", "15", "18" ]
A
<image>Find x.
32.2
1,682
[ "7.0", "16.6", "32.2", "35.5" ]
C
<image>Find the measure of $\angle 2$ if $m \angle D G F=53$ and $m \angle A G C=40$.
50
2,082
[ "37", "40", "50", "53" ]
C
<image>Find the rhombus of the kite.
240
2,052
[ "120", "180", "240", "300" ]
C
<image>Use rhombus XYZW with $m \angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\frac{5 a+1}{4}$ Find XZ
8
1,620
[ "2", "4", "8", "16" ]
C
<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth.
30.4
1,101
[ "25", "28.5", "30.4", "50" ]
C
<image>What is ED?
not enough information
1,637
[ "15", "25", "88.5", "not enough information" ]
D
<image>If $P T=y-3, P S=y+2, R S=12,$ and $Q S=16$ solve for $y$
\frac { 14 } { 3 }
1,925
[ "\\frac { 3 } { 14 }", "\\frac { 2 } { 3 }", "\\frac { 3 } { 2 }", "\\frac { 14 } { 3 }" ]
D
<image>The diagonals of rhombus FGHJ intersect at K. If $m\angle FJH = 82$, find $m\angle KHJ$.
49
265
[ "15", "33", "49", "82" ]
C
<image>$\Delta EFG$ is equilateral, and $\overline{E H}$ bisects $\angle E$. Find $x$.
6
71
[ "5", "6", "7", "8" ]
B
<image>Find y
4 \sqrt { 3 }
1,383
[ "2 \\sqrt { 3 }", "4", "4 \\sqrt { 3 }", "8" ]
C
<image>Find x.
4 \sqrt { 13 }
1,097
[ "4 \\sqrt { 5 }", "4 \\sqrt { 13 }", "8 \\sqrt { 5 }", "8 \\sqrt { 13 }" ]
B
<image>Find the area of the figure.
54.9
1,824
[ "22.9", "29.7", "54.9", "60" ]
C
<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\angle ABD = 55$ . Find $m\angle BDA$
55
1,455
[ "9", "12", "20", "55" ]
D
<image>$\triangle LMN \cong \triangle QRS$. Find $y$.
50
1,430
[ "10", "20", "40", "50" ]
D
<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure.
\frac { 3 } { 2 }
108
[ "\\frac { 4 } { 9 }", "\\frac { 2 } { 3 }", "\\frac { 3 } { 2 }", "\\frac { 9 } { 4 }" ]
C
<image>Quadrilateral MNOP is a rhombus. Find $m\angle MRN $
90
849
[ "56", "90", "124", "140" ]
B
<image>Find x. Round the side measure to the nearest tenth.
8.3
614
[ "4.2", "8.3", "16.7", "69.4" ]
B
<image>Find x. Assume that segments that appear to be tangent are tangent.
9.6
597
[ "6", "8", "9.6", "14.6" ]
C
<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary.
14.4
1,508
[ "14.4", "16", "28.8", "32" ]
A
<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary.
164
1,796
[ "82", "164", "836", "1448" ]
B
<image>Find $m\angle K$
62
1,041
[ "62", "72", "116", "160" ]
A
<image>Find $m \angle 2$.
23
1,913
[ "23", "55", "63", "125" ]
A
<image>Find $z$ in the figure.
13.5
1,172
[ "13.5", "14", "14.5", "15" ]
A
<image>Find $x$.
11
608
[ "9", "11", "37", "47" ]
B
<image>Quadrilateral ABCD is a rectangle. Find y
5
1,910
[ "5", "12", "24", "25" ]
A
<image>Find the measure of $\angle 1$.
55
140
[ "33", "45", "54", "55" ]
D
<image>Refer to trapezoid $CDFG$ with median $\overline{HE}$. Let $\overline{WX}$ be the median of $CDEH$. Find $WX$.
42
537
[ "34", "38", "42", "46" ]
C
<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear to be tangent are tangent.
5
263
[ "5", "10", "15", "20" ]
A
<image>Find the area of the shaded region.
50.3
2,087
[ "12.6", "50.3", "100.5", "402.1" ]
B
<image>For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$.
4
745
[ "4", "8", "26", "30" ]
A
<image>Find AX if $E X=24$ and $D E=7$
24
478
[ "1", "7", "24", "25" ]
C
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
315.2
1,409
[ "80.0", "157.6", "315.2", "364.0" ]
C
<image>What is the area of the triangle? Round your answer to the nearest tenth if necessary.
161.3
1,601
[ "137.4", "161.3", "170.5", "186.9" ]
B
<image>Find $m \angle K$.
46
930
[ "46", "63", "69", "92" ]
A
<image>Find the area of the parallelogram. Round to the nearest tenth if necessary.
106.1
1,345
[ "75", "106.1", "150", "212.1" ]
B
<image>Find $y$ in the figure.
15
406
[ "15", "34", "67", "75" ]
A
<image>For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$
8
2,056
[ "8", "16", "20", "32" ]
A
<image>Find x.
24 \sqrt { 2 }
2,044
[ "24", "24 \\sqrt { 2 }", "36", "24 \\sqrt { 3 }" ]
B
<image>In $\odot F$, find $m \widehat {ADB}$.
243
286
[ "63", "153", "233", "243" ]
D
<image>Find the perimeter of the figure. Round to the nearest tenth if necessary.
54.8
934
[ "54.8", "60", "80", "109.6" ]
A
<image>In the figure, $ \overline{JM} \cong \overline{PM}$ and $ \overline{ML} \cong \overline{PL}$. If $m \angle PLJ=34$, find $m \angle JPM$.
36.5
782
[ "34", "34.5", "36", "36.5" ]
D
<image>The segment is tangent to the circle. Find $x$.
4
1,579
[ "3", "4", "5", "8" ]
B
<image>Find the radius of $\odot K$. Round to the nearest hundredth.
19.00
2,069
[ "9.50", "19.00", "56.37", "59.69" ]
B

This dataset was converted from https://github.com/lupantech/InterGPS using the following script.

import os
import json
from PIL import Image
from datasets import Dataset, DatasetDict, Sequence
from datasets import Image as ImageData


MAPPING = {"A": 0, "B": 1, "C": 2, "D": 3}


def generate_data(data_path: str):
    for folder in os.listdir(data_path):
        folder_path = os.path.join(data_path, folder)
        image = Image.open(os.path.join(folder_path, "img_diagram.png"), "r")
        with open(os.path.join(folder_path, "data.json"), "r", encoding="utf-8") as f:
            data = json.load(f)
            yield {
                "images": [image],
                "problem": "<image>" + data["annotat_text"],
                "answer": data["choices"][MAPPING[data["answer"]]],
                "id": data["id"],
                "choices": data["choices"],
                "ground_truth": data["answer"],
            }


def main():
    trainset = Dataset.from_generator(generate_data, gen_kwargs={"data_path": os.path.join("data", "geometry3k", "train")})
    valset = Dataset.from_generator(generate_data, gen_kwargs={"data_path": os.path.join("data", "geometry3k", "val")})
    testset = Dataset.from_generator(generate_data, gen_kwargs={"data_path": os.path.join("data", "geometry3k", "test")})
    dataset = DatasetDict({"train": trainset, "validation": valset, "test": testset}).cast_column("images", Sequence(ImageData()))
    dataset.push_to_hub("hiyouga/geometry3k")


if __name__ == "__main__":
    main()
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