Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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convert the angle -2 radians to degrees, rounding to the nearest 10th.
\( -114.6^\circ \)
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convert the angle 4.5 radians to degrees, rounding to the nearest 10th.
\( 257.8^\circ \)
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10. maintain accuracy a certain rectangle has a perimeter of 10 units a…
The two pairs of possible missing vertices are $\boldsymbol{(3, 7)}$ and $\boldsymbol{(3, 4)}$, or $\boldsymbol{(-1, 7)}$ and $\boldsymbol{(-1, 4)}$
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practice: pythagorean theorem & ratios solve for the missing side using…
1. $c=15$ 2. $b=7$ 3. $a=80$
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convert the following angle from degrees to radians. express your answe…
\(2\pi\)
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9. build perseverance mrs. palmer is placing a retaining wall around a …
36 feet ### Justification: The vertices form a rectangle. First, calculate the side lengths in grid units using the difference in coordinates: vertical sides span 4 grid units, ho…
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convert the angle \\(\frac{19pi}{12}\\) radians to degrees.
$285^\circ$
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convert the following angle from degrees to radians. express your answe…
$\frac{17\pi}{12}$
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convert the angle -5 radians to degrees, rounding to the nearest 10th.
\( -286.5^\circ \)
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convert the following angle from degrees to radians. express your answe…
$\frac{29\pi}{12}$
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convert the angle -3.5 radians to degrees, rounding to the nearest 10th.
\( -200.5^\circ \)
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convert the following angle from degrees to radians. express your answe…
$\frac{41\pi}{12}$
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the diagram shows a triangle. what is the value of x? x = \\(\\square\\…
$57$
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8. draw and label the coordinates of a rectangle on the coordinate plan…
A rectangle with vertices at $\boldsymbol{(0,0)}$, $\boldsymbol{(5,0)}$, $\boldsymbol{(5,4)}$, and $\boldsymbol{(0,4)}$ (drawn and labeled on the coordinate plane, with area $5 \t…
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the diagram shows a triangle. what is the value of t? t = \\square^\\ci…
$7$
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convert the angle 2 radians to degrees, rounding to the nearest 10th.
\(114.6\) degrees
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the diagram shows a triangle. what is the value of w? w = \\square^\\ci…
$16$
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7. the map of the science center is shown. it shows where to find the t…
108 square meters
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the diagram shows a triangle. (an image of a triangle with angles 61°, …
$17$
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6. rectangle wxyz has consecutive vertices w(-9, -3), x(-9, 5), y(-2, 5…
Perimeter: $30$, Area: $56$
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triangle def was dilated according to the rule $d_{o,\frac{1}{3}}(x,y) …
- ∠F corresponds to ∠F' - Segment EE' is parallel to segment FF' - The distance from point D' to the origin is \(\frac{1}{3}\) the distance of point D to the origin (or also inclu…
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5. rectangle abcd has consecutive vertices a(-4, -6), b(-4, -1), c(3, -…
Perimeter: 24 Area: 35
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if $\\angle rts \\cong \\angle rtu$ and $rs = 73$, what is $ru$? $ru = …
73
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4. esperanza is building a rectangular table for her mother. she needs …
She will need 14 feet of wood for the frame, and 12 square feet of tiles for the tabletop.
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what is $m\\angle rst$? (there is a geometric figure with right angles …
$136^\circ$
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3. jason is preparing his garden for the winter. he will be constructin…
He will need 24 feet of fencing. The area of the ground covered by the tarp is 32 square feet.
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2. rectangle abcd has consecutive vertices a(-7, 2), b(-7, 8), and c(-3…
$(-3, 2)$
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given m∥n, find the value of x. (9x+4)° (2x-11)° answer attempt 1 out o…
$x = 17$
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1. rectangle wxyz has consecutive vertices x(6, -3), y(6, -10), and z(3…
$(3, -3)$
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quadrilateral qrst is dilated and translated to form similar figure qrs…
\(\frac{1}{2}\)
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19. geometry the sides of the hexagon shown are equal in length. the pe…
The possible side lengths are all positive real numbers less than or equal to 7 inches, or $0 < s \leq 7$ inches.
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circle the equations for which 6 is a solution of the equation. $4x=2$ …
To determine for which equations 6 is a solution, we substitute \( x = 6 \) (or the relevant variable) into each equation and check if it holds true. Let's analyze each equation: …
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look at the diagram. which term describes \\(\\overline{ce}\\)? median …
angle bisector
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∠qrt is a right angle. which term describes \\(\\overline{tr}\\)? perpe…
altitude
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(angle swt) is a right angle and (overline{vw} cong overline{sw}). whic…
median
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what is the image point of (-8, -9) after a translation left 3 units an…
$(-11, -14)$
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∠cbd ≅ ∠dbe. which term describes \\(\\overline{bd}\\)? options: altitu…
angle bisector
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figure nop is the result of a transformation on figure kjm. which trans…
A reflection over the y-axis
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look at the diagram. which term describes \\(\\overline{eg}\\)? angle b…
altitude
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date: 1. use the diagram to answer the following questions. a) how many…
5 ### Part (b)
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complete the following sentence. the figure below has does not have y r…
has rotational symmetry.
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question what is the image of (5, -5) after a dilation by a scale facto…
$(15, -15)$
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the convex polygon below has 8 sides. find the value of x. 140° 118° 12…
$x = 56$
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question point d is located at (3, -4) on the coordinate plane. point d…
$(-3, -4)$
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the measure of each interior angle of a regular polygon is 150°. find t…
12
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the sum of the interior angle measures of a convex polygon is $2340^{ci…
15
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the sum of the interior angle measures of a convex polygon is $1800^{ci…
12
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find the measure of each interior angle and each exterior angle of a re…
Measure of each interior angle = $160^\circ$ Measure of each exterior angle = $20^\circ$
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find the sum of the interior angle measures of a convex nonagon (a nine…
$1260$
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incorrect your answer is incorrect. find the value of x. (there is a qu…
$x = 75$
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find the value of x. (there is a quadrilateral with angles 131°, 86°, 6…
$85$
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question what is the image of (8, 0) after a dilation by a scale factor…
$(40, 0)$
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find the value of x. (image of a quadrilateral with angles 104°, 72°, 1…
$52^\circ$
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1 in the diagram of $\\triangle abc$ below, $\\overline{ab} \\cong \\ov…
The measure of \( \angle A \) is \( 100^\circ \) (or if finding \( \angle C \), it's \( 40^\circ \); adjust based on the actual question, but assuming finding \( \angle A \) here).
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find the sum of the interior angle measures of a convex 19-gon (a ninet…
$3060$
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find the sum of the interior angle measures of a convex 13-gon (a thirt…
$1980$
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2 the accompanying diagram shows the roof of a house that is in the sha…
\( 48^\circ \)
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the convex polygon below has 7 sides. find the value of x. (the polygon…
$126^\circ$
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question what is the image point of (-2, -3) after a translation right …
$(0, 1)$
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a side of the triangle below has been extended to form an exterior angl…
$x = 20$
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a side of the triangle below has been extended to form an exterior angl…
$52$
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complete the following sentence. the figure below has rotational symmet…
The figure below has **4-fold** rotational symmetry. $\boldsymbol{90^\circ}$ is the smallest possible rotation that results in the figure being mapped onto itself.
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a side of the triangle below has been extended to form an exterior angl…
$39$
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a side of the triangle below has been extended to form an exterior angl…
$34$
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on a flat field, jerry walks 80 m south from a to b. jerry then walks 1…
The bearing of B from A is \(180^\circ\) (or "south" in non - standard bearing terms, but the standard 3 - figure bearing is \(180^\circ\)). ### Part (b)
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which transformation would accomplish this? answer a reflection over th…
A rotation 90° clockwise about the origin
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a side of the triangle below has been extended to form an exterior angl…
$57^\circ$
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question point u is located at (5, 2) on the coordinate plane. point u …
$(-5, -2)$
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tress \try\ to test a translation or sequences of translations. a trans…
5 units right and 3 units down
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what is the image point of (-1,8) after a translation right 1 unit and …
$(0, 10)$
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what is the image of (1, -3) after a dilation by a scale factor of 3 ce…
$(3, -9)$
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11) 12) 13) 14) 15) ( mangle2 = x + 94 ) 16) ( mangle2 = 4x - 2 ) 17) (…
\(x = 12\)
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3) 6 x 4) x=6 4 x 5) 40° x 6) x 76° 7) 54° x 8) x 75° 9) 68° x 10) 20° x
\( x = 6 \) ### Problem 4:
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22. consider the system of equations. $y = -\\frac{1}{2}x + 6$ $y = 3x …
D (6, 3)
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ept equation. 8. ( x - y = 5 )
$y = x - 5$
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7. x + 2y = 4
- Solved for \( x \): \( x = 4 - 2y \) - Solved for \( y \): \( y = 2 - \frac{x}{2} \) (or \( y = \frac{4 - x}{2} \))
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is the following statement true or false? a plane is zero - dimensional…
false
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is the following statement true or false? the intersection of two plane…
false
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is the following statement true or false? two lines in a plane are eith…
false
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is the following statement true or false? a point is two - dimensional.…
false
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is the following statement true or false? parallel lines intersect in e…
false
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is the following statement true or false? perpendicular lines do not in…
false
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is the following statement true or false? either two lines in a plane a…
true
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is the following statement true or false? the intersection of a plane a…
false
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is the following statement true or false? the intersection of a plane a…
true
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is the following statement true or false? a plane extends forever. true…
true
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is the following statement true or false? a plane and a line can inters…
true
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a circle the context clues that help you determine the meaning of each …
1. Context clue: "You cannot eat it because it is poisonous" Meaning: Not fit or safe to be eaten 2. Context clue: "She could not figure out how to solve it" Meaning: Utterly bewi…
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reading: context clues activity reading: context clues practice context…
### Section A 1. Context clue: "cannot eat it because it is poisonous" Meaning: not fit or safe to eat 2. Context clue: "could not figure out how to solve it" Meaning: confused or…
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1. circle the correct answer. a. \\(\\frac{1}{2} + \\frac{5}{12}\\) gre…
1. a. less than 1 b. greater than 1 c. less than $\frac{1}{2}$ d. greater than $\frac{1}{2}$ 2. $<$
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10. part a how does the mother’s perspective about the neighboring stre…
B. He questions his mother’s concerns. ### Part B
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c. $c = 2pi r$ for $r$
$r = \frac{C}{2\pi}$
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consider parallelogram wxyz below. note that wxyz has vertices w(-2, -6…
(a) Length of $\overline{WX}$: $2\sqrt{29}$ Length of side adjacent to $\overline{WX}$: $\sqrt{29}$ (b) Slope of $\overline{WX}$: $\frac{5}{2}$ Slope of side adjacent to $\overlin…
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consider parallelogram wxyz below. note that wxyz has vertices w(1, -5)…
(a) Length of $\overline{XY}$: $\sqrt{65}$ Length of side adjacent to $\overline{XY}$: $\sqrt{65}$ (b) Slope of $\overline{XY}$: $\frac{7}{4}$ Slope of side adjacent to $\overline…
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consider parallelogram g h j k below. note that g h j k has vertices g …
(a) Slope of $\overline{GH}$: $-\frac{7}{3}$ Slope of side adjacent to $\overline{GH}$: $\frac{1}{5}$ (b) Length of $\overline{GH}$: $\sqrt{58}$ Length of side adjacent to $\overl…
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an acute triangle has two sides measuring 8 cm and 10 cm. what is the b…
B. \(6 < s < 12.8\)
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angela is building the wooden framework for the roof of a house. she ne…
It is an obtuse triangle. About 0.8 foot needs to be removed from the 20 foot board to create a right triangle.
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Question was provided via image upload.
Yes ### Part (b)
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an acute triangle has sides measuring 10 cm and 16 cm. the length of th…
\(6 < x < 26\) (assuming the last option in the image is \(6 < x < 26\), as per the triangle inequality and the steps above)
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Question was provided via image upload.
To determine if the HL (Hypotenuse - Leg) Congruence Property can be used, we recall that the HL Congruence Theorem states that if the hypotenuse and one leg of a right triangle a…