Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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what is the slope of the line that passes through the points (5, -1) an…
\(-\frac{1}{2}\) (corresponding to the option: \(-\frac{1}{2}\))
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multiple choice 10 points where does the point (3, -5) lie in relation …
Inside the circle (the option: Inside the circle)
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determine the triangle similarity theorem for each triangle pair below.…
s (Selected Problems) - **Problem 10**: \( x = 4 \) - **Problem 11**: \( x = 8 \) - **Problem 14**: \( S = 48 \) (or \( SB = 36 \), depending on interpretation) - **Problem 15**: …
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the slope of the line determined by the points (-3, 2) and (2, -3) is z…
\(-1\) (corresponding to the option with \(-1\))
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2/13 this system has ______ solutions 0 2 1 infinitely many
1 (and the option corresponding to "1" among the choices, e.g., if the options are as shown with "1" as a choice, the answer is the option with "1" text)
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multiple choice 10 points which is the equation of a circle whose cente…
\(x^2 + y^2 = 34\) (the option with this equation)
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multiple choice 10 points a circle has the equation ((x - 3)^2 + (y + 5…
The y - coordinate of the center is 5.
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which of the following can be measured? line angle point ray
B. angle
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question 1 of 10 find m\\overline{bc} in \\triangle abc.
$8\sqrt{2}$
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which two angle measurements (in degrees) are complementary? 42 and 48 …
A. 42 and 48
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use the given information to complete the proof of the following theore…
- Statement 3: \( \angle 1 \cong \angle 3 \) - Statement 4: \( \overline{XZ} \cong \overline{XZ} \) - Statement 5: \( \triangle WXZ \cong \triangle YZX \), Reason: SAS Congruence …
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find the missing measurement. round your answer to the nearest tenth. a…
$6.7$ cm
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multiple choice 10 points a circle has the equation ((x + 5)^2 + (y - 2…
\((-5, 2)\)
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multiple choice 10 points a circle has the equation $x^2 + y^2 = 16$. w…
4 (corresponding to the option with "4" as the text, e.g., if the option is labeled as, say, C. 4, then the answer would be C. 4)
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find the area. exact answers, no rounding. 11 in area = 17.4 sq in 5.8 …
31.9 sq in
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using the given figure, determine the length of \\(\\overline{pr}\\) if…
17 units
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what is the surface area? 15 in 15 in 15 in square inches
1350
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given that \\( \\overline{de} \\) is a perpendicular bisector of \\( \\…
\(CE = BC\) (the statement that is not true)
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what is the surface area? 14 m 14 m 14 m square meters
1176 square meters
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use the given information to complete the proof of the following theore…
- Step 8 Reason: If alt. int. \( \angle s \cong \), then lines \( \parallel \) - Step 9 Reason: A quadrilateral with both pairs of opposite sides parallel is a parallelogram (by d…
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what is the surface area? 1 cm, 6 cm, 2 cm square centimeters
40 square centimeters
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find the area of the shaded region
$x^2 - 3x + 36$
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find d. write your answer in simplest radical form. yards
20 yards
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19) dilation of 2 about the origin
The dilated coordinates are \( L'(-4, 0) \), \( J'(0, -2) \), and \( K'(4, 2) \). To graph the dilated triangle, plot these points and connect them.
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what is the measure of angle 1 in the figure below? 80° 60° 40° 30°
\(60^\circ\) (corresponding to the option with \(60^\circ\))
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which of the following is a pair of complementary angles?
The first pair of angles (the top - first option) are complementary angles (since their sum is \(90^\circ\)). So the correct option is the first one (the top - first circle with t…
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18) dilation of 1.5 about the origin
The dilated triangle has vertices at \( J'(-3,4.5) \), \( K'(4.5,0) \), and \( L'(0,-1.5) \). To draw the dilated figure, plot these points and connect them. (Note: The actual plo…
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apply cavalieris principle the following figures all have the same heig…
A. Only A and B
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consider the following cylinder and cone. marcel tried to use cavalieri…
B. It isn't true that corresponding cross-sections have the same area.
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list the intercepts of the graph shown on the right. the intercept(s) i…
$(-7, 0)$, $(0, -2)$, $(2, 0)$, $(7, 0)$
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using the diagram, identify the dashed line segment. perpendicular bise…
C. median
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what is the slope of this line? simplify your answer and write it as a …
\(-\frac{5}{3}\)
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using the given figure, find the length of \\(\\overline{de}\\) if \\(\…
1 unit
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name a segment that is an angle bisector of the given figure.\\(\\overl…
\(\boldsymbol{\overline{AE}}\) (corresponding to the option with \(\overline{AE}\))
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4） what is the area of the triangle? □ square centimeters
6 square centimeters
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a rectangular board is 1100 millimeters long and 900 millimeters wide. …
\( 0.99\space \text{m}^2 \)
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in a plane, lines that never meet are called ______. perpendicular inte…
D. parallel
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1 yard 8 yards what is the area of the triangle? □ square yards
4 square yards
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find p. write your answer in simplest radical form. kilometers submit w…
$3\sqrt{3}$ kilometers
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the perpendicular bisector of a line segment does which of the followin…
D. identifies the midpoint of the line segment (assuming the options are labeled A, B, C, D as per the order: first option A, second B, third C, fourth D)
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find c. write your answer in simplest radical form. yards submit work i…
$28\sqrt{3}$ yards
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find n. 8√2 mm 45° 45° n write your answer in simplest radical form. bl…
16 millimeters
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which of the following statements about a bisector is true? it creates …
It creates two equal angles or line segments
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using trigonometry to find lengths find the missing side. round to the …
\(4.7\) ### Problem 3:
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find s. write your answer in simplest radical form. meters
$4\sqrt{3}$ meters
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4 ft 5 ft what is the area of the triangle? square feet
10 square feet
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3. if the medium rectangle represents $10^5$, then what does the large …
### Problem 3 (Large Square and Small Square when Medium Rectangle is \(10^5\)) Assuming the medium rectangle is a product of a small square and a large square (or related by expo…
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a science fair poster is a rectangle 48 inches long and 36 inches wide.…
12 square feet (or $12\ \text{ft}^2$)
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angles 1 and 3 are ______? right supplementary complementary vertical
vertical (the option corresponding to "vertical")
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8. find the surface area of the following figure. round to the nearest …
$205.8$ $\text{mi}^2$
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find j. write your answer in simplest radical form. miles submit pythag…
$5\sqrt{3}$ miles
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∠1 and ∠2 are called ______. supplementary angles vertical angles compl…
supplementary angles
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solve the inequality graph the solution. |2x + 3| - 14 ≤ -1 select the …
A. The solution is $\boldsymbol{-8 \leq x \leq 5}$ *(For the graph: Draw a number line, place closed circles at -8 and 5, and shade the region between these two points.)*
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22.) a=???, b= 9, c=√97
$a = 4$
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21.) a = 3, b = ???, c = \\sqrt{58}
\(b = 7\)
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20.) a=6, b=2√7, c=??
\(c = 2\sqrt{2}\) (If \(a\) is the hypotenuse) or if \(c\) is the hypotenuse, using \(c^{2}=a^{2}+b^{2}=36 + 28 = 64\), then \(c = 8\). Since \(a=6\) and \(b = 2\sqrt{7}\approx5.2…
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which equation can be used to solve for b? triangle image with right an…
$\boldsymbol{\tan(30^\circ) = \frac{5}{b}}$ (the first option)
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18.) a= 3√3, b= 3, c= ???
\(c = 6\)
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which relationship in the triangle must be true? a c b c b a ○ sin(b) =…
\(\sin(B)=\cos(90 - B)\) (the second option)
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what is the length of $overline{ac}$? round to the nearest tenth. a tri…
10.5 m
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17.) a=2, b=2√3, c=???
\(c = 4\)
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3. draw a right angle 4. 83,407 ○ 83,470 5. 8 + 3 = ? 8. what is the an…
6. $83,407 < 83,470$ 7. $11$ 8. Quotient 9. $6$ 10. $1,060,273$ 11. Odd 12. A 5-sided closed polygon (as sketched) 13. $2,621$ 14. $3$ 15. 2 grams 16. $23,008$ 17. $28,000$ 18. $\…
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36. graph the image of tuv after the following sequence of transformati…
The coordinates of the final image are $T'(-4, 12)$, $U'(-12, 9)$, $V'(-8, 5)$. Plot these points and connect them to form the transformed triangle.
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34. on a coordinate plane, vertex a for triangle abc is located at (6,4…
A.) (3, 2)
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35. lily wants to define a transformation (or series of transformations…
A.) It can be defined with two reflections.
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1. use the graph to answer parts (a)-(f). a. write the coordinates of p…
a. $(-1, -5)$ b. $(-1, 5)$ c. $(1, -5)$
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e. explain the relationship between the coordinates of point a and poin…
2a. $(-5, -2)$ 2b. $(-5, 2)$ Note: Parts e and f cannot be solved as the coordinates of point A and point C are not provided in the image. Please share those coordinates to answer…
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14. a pocket veto is a check on the legislative branch or executive bra…
Legislative Branch
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8) in rectangle abcd, diagonals ac and bd intersect at point e. if ae =…
\( x = 21 \)
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which three of these ages can a person be to set up an account? 13 14 1…
13, 14, 19 ### Sub - question 2: Does the graph of \(x\geq13\) have an open circle or a closed circle at 13?
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state the rule that was used to translate $\\triangle abc$ to $\\triang…
\( (x, y) \to (x + 4, y - 8) \) (Wait, but maybe the actual shift is different. Wait, maybe I misread the graph. Alternatively, maybe the horizontal shift is 4 and vertical shift …
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suppose you are given a triangle with the following coordinates, a(0, 0…
\(A'(-2,1)\) \(B'(0,4)\) \(C'(-1,-1)\)
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translate △abc using the rule (x, y) → (x + 6, y - 3) to form △abc. wha…
- \( A(2, 3) \), \( A'(8, 0) \) - \( B(-2, -1) \), \( B'(4, -4) \) - \( C(-1, 4) \), \( C'(5, 1) \)
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the solid below is made from cubes. find its volume. 1 cm
18 $\text{cm}^3$
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4 the coordinates for three vertices of a rectangle are (2, 2), (8, 2),…
b. \((8,6)\) (assuming the typo in the original option b, if the original option b is \((8,6)\)) ### Question 5
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in the diagram below, \\(\\overline{ab} \\cong \\overline{bc}\\), and \…
$\boldsymbol{m\angle BCD = 116^\circ}$ Reason: Supplementary angles form a straight angle
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the exterior angle of a regular polygon measures 8°. how many sides doe…
45
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the solid below is made from cubes. find its volume. 1 in
\( 12 \)
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1 what are the x and y coordinates for point d on the graph shown? a. (…
c. \((6,4)\) ### Question 2
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the solid below is made from cubes. find its volume. 1 cm \\square cm^3
\(18\)
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why do adults complain so much? find the length of the hypotenuse of ea…
\( 5 \) (corresponds to letter \( E \))
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14. what is the area of the parallelogram? a. 14 mi² b. 28 mi² c. 56 mi…
14. A. $14\ \text{mi}^2$ 15. $63$ square inches 16. A. $54\ \text{mm}^2$ 17. $58\ \text{mm}^2$
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what is the area of the triangle? 9 mm 8 mm square millimeters
36 square millimeters
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4 ) figure 1 can be transformed to create figure 2 using a single trans…
C. Reflection ### Question 5
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examine the diagram. which is the height of the triangle? a. 40 m b. 60…
C. 80 m
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an architect is designing a new windmill with four sails. in her sketch…
\((6, -5)\)
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windmill: an architect is designing a new windmill with four sails. in …
\((9, 2)\)
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read this passage from a british newspaper. the french and indians, the…
The British panicked when they were shot at.
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windmill an architect is designing a new windmill with four sails. in h…
\((3, - 4)\)
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the rule ((x,y)\to(x + 3,y)) is used to transform quadrilateral (jklm),…
The coordinates of \( K' \) are \( (5,5) \)
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find the tangent of $\\angle y$. simplify your answer and write it as a…
\(\frac{55}{48}\)
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1 ) if triangle abc is rotated 90° clockwise about the origin, what wil…
B. (1, 4) ### Question 2
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which shape is a parallelogram?
The top - left shape (the rhombus - like quadrilateral) is a parallelogram.
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in the figure below, points d, e, and f are the midpoints of the sides …
$AB = 68$ $DE = 36$ $BE = 34$
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in the figure below, points s, t, and u are the midpoints of the sides …
$QR = 24$ $QT = 12$ $ST = 35$
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a rectangle has vertices at $(-2, 1)$, $(3, 1)$, $(3, -2)$, and $(-2, -…
D. 15 square units
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the actual lengths of the garden are shown in the table. choose an equi…
The equivalent ratio of scale drawing length to actual garden length is $\frac{1}{48}$ (or 1 in : 48 in, which simplifies to 1 in : 4 ft)
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for each part below, use the figure to fill in the blank. if necessary,…
(a) $m\angle Q = 65^\circ$ (b) $m\angle M = 60^\circ$
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find the area. a. 1818 sq cm b. 1406 sq cm c. 1246 sq cm d. 141 sq cm e…
C. 1246 sq cm
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find the slope of the line passing through the points (-9, -3) and (7, …
$\frac{-1}{4}$