chenhegu/geo3k · Datasets at Hugging Face

images images listlengths 1 1	prompt listlengths 1 1	label stringlengths 1 34
	[ { "content": "<image>Find x. Round to the nearest tenth, if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	11
	[ { "content": "<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. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	5:9
	[ { "content": "<image>Find the value of $f$ in the parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	14
	[ { "content": "<image>Find the value of the variable $y$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	125
	[ { "content": "<image>Find $m\\angle S$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	123
	[ { "content": "<image>Find $x$ so that $ m \\parallel n $. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	13
	[ { "content": "<image>Find $ m ∠RSU $ so that $ m \\parallel n $. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	124
	[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	12
	[ { "content": "<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 $B C=31.2$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	78
	[ { "content": "<image>$\\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the diameter of the circle. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	17
	[ { "content": "<image>Find $\\angle 10$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	50
	[ { "content": "<image>Find the measure of $\\angle 7$ if $\\overline{A B} \\perp \\overline{B C}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	140
	[ { "content": "<image>Find $m \\widehat {CF}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	80
	[ { "content": "<image>$\\overline{BC} \\\| \\overline{DF}$. $AC=15$, $BD=3x-2$, $CF=3x+2$, and $AB=12$. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	6
	[ { "content": "<image>Each pair of polygons is similar. Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	70
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	12
	[ { "content": "<image>Quadrilateral ABCD is a rectangle. If $m\\angle ADB = 4x + 8$ and $m\\angle DBA = 6x + 12$, find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	7
	[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	2
	[ { "content": "<image>Find x You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	22
	[ { "content": "<image>Find x. Assume that any segment that appears to be tangent is tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	13
	[ { "content": "<image>Find the perimeter of quadrilateral ABCD. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	40 + 14 \sqrt { 2 }
	[ { "content": "<image>Find $EG$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	10
	[ { "content": "<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.\r\n You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	7
	[ { "content": "<image>Find $ST$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	5
	[ { "content": "<image>Find the measure of the altitude drawn to the hypotenuse. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	\sqrt { 612 }
	[ { "content": "<image>Use parallelogram $ABCD$ to find $AB$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	12
	[ { "content": "<image>Find the area of the figure. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	39.4
	[ { "content": "<image>Find $x$ if $\\odot M \\cong \\odot N$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	9
	[ { "content": "<image>Find x. Round side measures to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	35.1
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	2 \sqrt { 5 }
	[ { "content": "<image>If $QT=11$, what is $QU$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	11
	[ { "content": "<image>$a=14, b=48,$ and $c=50$ find $tanA$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	0.29
	[ { "content": "<image>Find $y$ so that the quadrilateral is a parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	41
	[ { "content": "<image>$\\ln \\odot K$, $ M N=16$ and $m \\widehat{M N}=98$. Find the measure of $LN$. Round to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	8.94
	[ { "content": "<image>In the figure, $QR \\\| TS$, $QT \\\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 6$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	131
	[ { "content": "<image>Find the measure of $m∠C$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	70
	[ { "content": "<image>Find x You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	7
	[ { "content": "<image>Find $m \\angle 2$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	39
	[ { "content": "<image>If PR \|\| WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	6
	[ { "content": "<image>Find z. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	12 \sqrt { 3 }
	[ { "content": "<image>WXYZ is a parallelogram. Find $m \\angle Y Z W$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	115
	[ { "content": "<image>Find $XZ$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	23
	[ { "content": "<image>Find y. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	10
	[ { "content": "<image>Find the measure of $\\angle 1$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	56
	[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	60
	[ { "content": "<image>Find the area of the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	150
	[ { "content": "<image>In $\\odot P, m \\widehat{E N}=66$ and $m \\angle G P M=89$ . \r\nFind $m \\angle G N M$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	44.5
	[ { "content": "<image>Find $x$ so that the quadrilateral is a parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	3
	[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	1520
	[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	3
	[ { "content": "<image>Find $y$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	3
	[ { "content": "<image>WXYZ is a parallelogram. Find $m \\angle X W Z$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	65
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	\frac { 15 \sqrt { 2 } } { 2 }
	[ { "content": "<image>Find $x$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	34
	[ { "content": "<image>Find the measure of $\\angle 1$ if $m \\angle D G F=53$ and $m \\angle A G C=40$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	37
	[ { "content": "<image>Find the measure of the altitude drawn to the hypotenuse. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	3 \sqrt { 5 }
	[ { "content": "<image>Chords $\\overline{JF}$ and $\\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	6
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	32.2
	[ { "content": "<image>Find the measure of $\\angle 2$ if $m \\angle D G F=53$ and $m \\angle A G C=40$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	50
	[ { "content": "<image>Find the rhombus of the kite. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	240
	[ { "content": "<image>Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\nFind XZ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	8
	[ { "content": "<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	30.4
	[ { "content": "<image>What is ED? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	not enough information
	[ { "content": "<image>If $P T=y-3, P S=y+2, R S=12,$ and $Q S=16$\r\nsolve for $y$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	\frac { 14 } { 3 }
	[ { "content": "<image>The diagonals of rhombus FGHJ intersect at K. \r\nIf $m\\angle FJH = 82$, find $m\\angle KHJ$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	49
	[ { "content": "<image>$\\Delta EFG$ is equilateral, and $\\overline{E H}$ bisects $\\angle E$. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	6
	[ { "content": "<image>Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	4 \sqrt { 3 }
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	4 \sqrt { 13 }
	[ { "content": "<image>Find the area of the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	54.9
	[ { "content": "<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find $m\\angle BDA$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	55
	[ { "content": "<image>$\\triangle LMN \\cong \\triangle QRS$. Find $y$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	50
	[ { "content": "<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	\frac { 3 } { 2 }
	[ { "content": "<image>Quadrilateral MNOP is a rhombus. Find $m\\angle MRN $ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	90
	[ { "content": "<image>Find x. Round the side measure to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	8.3
	[ { "content": "<image>Find x. Assume that segments that appear to be tangent are tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	9.6
	[ { "content": "<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	14.4
	[ { "content": "<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	164
	[ { "content": "<image>Find $m\\angle K$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	62
	[ { "content": "<image>Find $m \\angle 2$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	23
	[ { "content": "<image>Find $z$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	13.5
	[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	11
	[ { "content": "<image>Quadrilateral ABCD is a rectangle. Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	5
	[ { "content": "<image>Find the measure of $\\angle 1$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	55
	[ { "content": "<image>Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{WX}$ be the median of $CDEH$. Find $WX$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	42
	[ { "content": "<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	5
	[ { "content": "<image>Find the area of the shaded region. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	50.3
	[ { "content": "<image>For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	4
	[ { "content": "<image>Find AX if $E X=24$ and $D E=7$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	24
	[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	315.2
	[ { "content": "<image>What is the area of the triangle? Round your answer to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	161.3
	[ { "content": "<image>Find $m \\angle K$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	46
	[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	106.1
	[ { "content": "<image>Find $y$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	15
	[ { "content": "<image>For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	8
	[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	24 \sqrt { 2 }
	[ { "content": "<image>In $\\odot F$, find $m \\widehat {ADB}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	243
	[ { "content": "<image>Find the perimeter of the figure. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	54.8
	[ { "content": "<image>In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=34$, find $m \\angle JPM$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	36.5
	[ { "content": "<image>The segment is tangent to the circle. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	4
	[ { "content": "<image>Find the radius of $\\odot K$. Round to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]	19.00

[ { "content": "<image>Find x. Round to the nearest tenth, if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

11

[ { "content": "<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. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

5:9

[ { "content": "<image>Find the value of $f$ in the parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

14

[ { "content": "<image>Find the value of the variable $y$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

125

[ { "content": "<image>Find $m\\angle S$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

123

[ { "content": "<image>Find $x$ so that $ m \\parallel n $. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

13

[ { "content": "<image>Find $ m ∠RSU $ so that $ m \\parallel n $. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

124

[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

12

[ { "content": "<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 $B C=31.2$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

78

[ { "content": "<image>$\\overline{AB}$ is a diameter, $AC=8$ inches, and $BC=15$ inches. Find the diameter of the circle. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

17

[ { "content": "<image>Find $\\angle 10$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

50

[ { "content": "<image>Find the measure of $\\angle 7$ if $\\overline{A B} \\perp \\overline{B C}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

140

[ { "content": "<image>Find $m \\widehat {CF}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

80

[ { "content": "<image>$\\overline{BC} \\| \\overline{DF}$. $AC=15$, $BD=3x-2$, $CF=3x+2$, and $AB=12$. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

6

[ { "content": "<image>Each pair of polygons is similar. Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

70

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

12

[ { "content": "<image>Quadrilateral ABCD is a rectangle. If $m\\angle ADB = 4x + 8$ and $m\\angle DBA = 6x + 12$, find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

7

[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

2

[ { "content": "<image>Find x You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

22

[ { "content": "<image>Find x. Assume that any segment that appears to be tangent is tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

13

[ { "content": "<image>Find the perimeter of quadrilateral ABCD. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

40 + 14 \sqrt { 2 }

[ { "content": "<image>Find $EG$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

10

[ { "content": "<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.\r\n You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

7

[ { "content": "<image>Find $ST$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

5

[ { "content": "<image>Find the measure of the altitude drawn to the hypotenuse. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

\sqrt { 612 }

[ { "content": "<image>Use parallelogram $ABCD$ to find $AB$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

12

[ { "content": "<image>Find the area of the figure. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

39.4

[ { "content": "<image>Find $x$ if $\\odot M \\cong \\odot N$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

9

[ { "content": "<image>Find x. Round side measures to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

35.1

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

2 \sqrt { 5 }

[ { "content": "<image>If $QT=11$, what is $QU$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

11

[ { "content": "<image>$a=14, b=48,$ and $c=50$ find $tanA$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

0.29

[ { "content": "<image>Find $y$ so that the quadrilateral is a parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

41

[ { "content": "<image>$\\ln \\odot K$, $ M N=16$ and $m \\widehat{M N}=98$. Find the measure of $LN$. Round to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

8.94

[ { "content": "<image>In the figure, $QR \\| TS$, $QT \\| RS$, and $m \\angle 1=131$. Find the measure of $\\angle 6$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

131

[ { "content": "<image>Find the measure of $m∠C$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

70

[ { "content": "<image>Find x You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

7

[ { "content": "<image>Find $m \\angle 2$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

39

[ { "content": "<image>If PR || WX, WX = 10, XY = 6, WY = 8, RY = 5, and PS = 3, find PQ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

6

[ { "content": "<image>Find z. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

12 \sqrt { 3 }

[ { "content": "<image>WXYZ is a parallelogram. Find $m \\angle Y Z W$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

115

[ { "content": "<image>Find $XZ$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

23

[ { "content": "<image>Find y. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

10

[ { "content": "<image>Find the measure of $\\angle 1$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

56

[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

60

[ { "content": "<image>Find the area of the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

150

[ { "content": "<image>In $\\odot P, m \\widehat{E N}=66$ and $m \\angle G P M=89$ . \r\nFind $m \\angle G N M$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

44.5

[ { "content": "<image>Find $x$ so that the quadrilateral is a parallelogram You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

3

[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

1520

[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

3

[ { "content": "<image>Find $y$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

3

[ { "content": "<image>WXYZ is a parallelogram. Find $m \\angle X W Z$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

65

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

\frac { 15 \sqrt { 2 } } { 2 }

[ { "content": "<image>Find $x$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

34

[ { "content": "<image>Find the measure of $\\angle 1$ if $m \\angle D G F=53$ and $m \\angle A G C=40$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

37

[ { "content": "<image>Find the measure of the altitude drawn to the hypotenuse. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

3 \sqrt { 5 }

[ { "content": "<image>Chords $\\overline{JF}$ and $\\overline{BC}$ intersect at $K .$ If $B K=8$, $K C=12,$ and $K F=16,$ find $J K$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

6

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

32.2

[ { "content": "<image>Find the measure of $\\angle 2$ if $m \\angle D G F=53$ and $m \\angle A G C=40$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

50

[ { "content": "<image>Find the rhombus of the kite. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

240

[ { "content": "<image>Use rhombus XYZW with $m \\angle W Y Z=53, V W=3$, $X V=2 a-2,$ and $Z V=\\frac{5 a+1}{4}$\r\nFind XZ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

8

[ { "content": "<image>Find the area of the shaded region. Assume that all polygons that appear to be regular are regular. Round to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

30.4

[ { "content": "<image>What is ED? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

not enough information

[ { "content": "<image>If $P T=y-3, P S=y+2, R S=12,$ and $Q S=16$\r\nsolve for $y$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

\frac { 14 } { 3 }

[ { "content": "<image>The diagonals of rhombus FGHJ intersect at K. \r\nIf $m\\angle FJH = 82$, find $m\\angle KHJ$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

49

[ { "content": "<image>$\\Delta EFG$ is equilateral, and $\\overline{E H}$ bisects $\\angle E$. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

6

[ { "content": "<image>Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

4 \sqrt { 3 }

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

4 \sqrt { 13 }

[ { "content": "<image>Find the area of the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

54.9

[ { "content": "<image>ABCD is a rhombus. If EB = 9, AB = 12 and $m\\angle ABD = 55$ . Find $m\\angle BDA$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

55

[ { "content": "<image>$\\triangle LMN \\cong \\triangle QRS$. Find $y$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

50

[ { "content": "<image>For the pair of similar figures, use the given areas to find the scale factor of the blue to the green figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

\frac { 3 } { 2 }

[ { "content": "<image>Quadrilateral MNOP is a rhombus. Find $m\\angle MRN $ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

90

[ { "content": "<image>Find x. Round the side measure to the nearest tenth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

8.3

[ { "content": "<image>Find x. Assume that segments that appear to be tangent are tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

9.6

[ { "content": "<image>Find the area of the figure in feet. Round to the nearest tenth, if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

14.4

[ { "content": "<image>Find the perimeter of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

164

[ { "content": "<image>Find $m\\angle K$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

62

[ { "content": "<image>Find $m \\angle 2$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

23

[ { "content": "<image>Find $z$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

13.5

[ { "content": "<image>Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

11

[ { "content": "<image>Quadrilateral ABCD is a rectangle. Find y You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

5

[ { "content": "<image>Find the measure of $\\angle 1$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

55

[ { "content": "<image>Refer to trapezoid $CDFG$ with median $\\overline{HE}$. Let $\\overline{WX}$ be the median of $CDEH$. Find $WX$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

42

[ { "content": "<image>Find x. Round to the nearest tenth if necessary. Assume that segments that appear\r\nto be tangent are tangent. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

5

[ { "content": "<image>Find the area of the shaded region. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

50.3

[ { "content": "<image>For trapezoid $R S T V, A$ and $B$ are midpoints of the legs. Find $V T$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

4

[ { "content": "<image>Find AX if $E X=24$ and $D E=7$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

24

[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

315.2

[ { "content": "<image>What is the area of the triangle? Round your answer to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

161.3

[ { "content": "<image>Find $m \\angle K$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

46

[ { "content": "<image>Find the area of the parallelogram. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

106.1

[ { "content": "<image>Find $y$ in the figure. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

15

[ { "content": "<image>For trapezoid $D E G H, X$ and $Y$ are midpoints of the legs. Find $D E$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

8

[ { "content": "<image>Find x. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

24 \sqrt { 2 }

[ { "content": "<image>In $\\odot F$, find $m \\widehat {ADB}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

243

[ { "content": "<image>Find the perimeter of the figure. Round to the nearest tenth if necessary. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

54.8

[ { "content": "<image>In the figure, $ \\overline{JM} \\cong \\overline{PM}$ and $ \\overline{ML} \\cong \\overline{PL}$. If $m \\angle PLJ=34$, find $m \\angle JPM$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

36.5

[ { "content": "<image>The segment is tangent to the circle. Find $x$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

4

[ { "content": "<image>Find the radius of $\\odot K$. Round to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\boxed{}.", "role": "user" } ]

19.00