Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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question find the distance between the two points in simplest radical f…
The distance between the two points is \( \boldsymbol{10} \).
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write an equation of the line below. your answer
\(y =-\frac{2}{5}x + 4\)
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5. triangle abc is taken to triangle abc by a dilation. which of these …
d. \( \frac{4}{3} \)
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$\\overline{wx} \\parallel \\overline{vy}$. find $vw$. $vw = \\square$ …
12
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given: ( l parallel m ); ( angle 1 cong angle 3 ) prove: ( p parallel q…
corresponding angles theorem
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triangle $\\triangle abc$ is the result of dilating $\\triangle abc$ ab…
The measures of $\angle B$ and $\angle B'$ are equal: True The coordinates of A and A' are the same: True
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classify the triangle using its angles. acute right obtuse
B. right (assuming the middle option is "right" as per the options: acute, right, obtuse)
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which of the following transformations carry this regular polygon onto …
The transformations that carry the regular polygon (equilateral triangle) onto itself are "rotation of \( 120^\circ \) counterclockwise" and "reflection across \( l \)".
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question 9 of 10 which descriptions from the list below accurately desc…
A. Proportional side lengths
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on the packaging for a triangular sail, the edge measurements for the s…
obtuse
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question 9 of 10 the triangles shown below must be congruent. a. true b…
A. True
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find the area of the figure below, composed of a rectangle and two semi…
\( 64.6 \)
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question 5 of 10 which of the following are remote interior angles of ∠…
C. ∠6, E. ∠4
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line segment st is dilated to create line segment st using the dilation…
\( x = 2.5 \) units (Option: \( x = 2.5 \) units)
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solve for x. round your answer to the nearest tenth if necessary. figur…
\( x = 31.6 \)
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the angle bisectors of $\\triangle abc$ are $\\overline{av}$, $\\overli…
\( UV = 4 \), \( m\angle SBT = 108^\circ \), \( m\angle SAV = 4^\circ \) Wait, but let's recheck: 1. \( UV \): Incenter is equidistant from all sides, so \( TV = UV = 4 \). Correc…
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find the length of the third side. if necessary, round to the nearest t…
8 (corresponding to the option "8")
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find the range of possible values for x. the range is \\(\\square < x <…
The range is \(3 < x < 34\). So the first box is \(3\) and the second box is \(34\).
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rectangle abcd is graphed in the coordinate plane. the following are th…
14
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write an equation for the circle graphed below.
\((x + 4)^2+(y + 2)^2 = 9\)
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the figure shows eight congruent triangles made by dividing a square th…
C. \( 8 \, \text{cm}^2 \)
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graph each equation. 9) \\(\\dfrac{x^2}{4} + \\dfrac{y^2}{9} = 1\\) gra…
The graph is an ellipse centered at the origin \((0,0)\), with vertices at \((0, 3)\) and \((0, - 3)\), and co - vertices at \((2, 0)\) and \((-2, 0)\). To draw it, plot these fou…
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point $c(-4, -3)$ is the image of $c(-2, -3)$ under a translation. dete…
A translation by \(2\) units left
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find the measure of the missing angle. answer attempt 1 out of 2 a = su…
\(20^{\circ}\)
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consider the following figure. (note that the figure is not drawn to sc…
$ED < CE < CD < BD < BC$
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given: \\(\\overline{am} \\cong \\overline{cp}\\), \\(\\overline{cm} \\…
1. Statement: \( \overline{AM} \cong \overline{CP} \); 2. Statement: \( \overline{CM} \cong \overline{GP} \); 3. Statement: \( \overline{AC} \cong \overline{CG} \), Reason: midpoi…
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in the diagram below, \\(\\overline{no}\\) is parallel to \\(\\overline…
\(MO = 18\)
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complete the proof that $\\triangle ghi \\cong \\triangle fej$. (image …
For statement 5, the reason is "Additive Property of Length"; for statement 6, the reason is "Substitution (using \( \overline{FG} \cong \overline{IJ} \) to replace \( IJ \) with …
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find the volume of the cone. either enter an exact answer in terms of π…
\( 12\pi \) (or \( 37.68 \))
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given $m \\parallel n$, find the value of $x$. (there is a diagram show…
\( x = 13 \)
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question find the area of the figure below, composed of a parallelogram…
\( 110.3 \)
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y = 8√3 simplify. find the values of x and y. give your answers in simp…
(Problem 5): \(x = 9\), \(y = 9\sqrt{3}\) ### Problem 6:
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9. δabc is similar to δdef. the lengths of the sides of δabc are 5, 8, …
The length of the shortest side of \( \triangle DEF \) is \( \boldsymbol{12.5} \) (or \( \boldsymbol{\frac{25}{2}} \)).
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7. as shown in the diagram below, $\\triangle abc \\sim \\triangle def$…
14
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6. if $\\triangle abc \\sim \\triangle efg$, $m\\angle c = 4x + 30$, an…
\( x = 20 \)
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5. in the diagram below, \\( \\overline{af} \\), and \\( \\overline{db}…
The length of \( \overline{CB} \) is \( 16.2 \).
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5. find the value of x with parallel lines that are cut by a transversa…
s: - For the first (left) diagram: \(x = 8\) - For the second (right) diagram: If we assume that \((17x + 4)^\circ\) and \(140^\circ\) are same - side interior angles (supplementa…
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graph this inequality: y > -4 plot points on the boundary line. select …
1. Draw a dotted horizontal line at \( y = - 4 \) (passing through points like (0, - 4), (1, - 4), (- 1, - 4) etc.). 2. Shade the region above the dotted line \( y=-4 \).
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graph this inequality: x > -3 plot points on the boundary line. select …
- Boundary line: Dotted vertical line at \( x = -3 \). - Shaded region: Area to the right of \( x = -3 \).
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why is partitioning a directed line segment into a ratio of 1:3 not the…
C. The ratio given is part to part. The total number of parts in the whole is \(1+3 = 4\).
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the midpoint of a line segment partitions the line segment into a ratio…
A. 1:1
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if point p is \\(\frac{9}{11}\\) of the distance from m to n, what rati…
A. 9:2
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problem 6 how many solutions does this system of equations have? one so…
One solution (the option: One solution)
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40. fill in the missing statements and reasons to complete the followin…
1. \( L \) is the midpoint of \( \overline{JN} \), \( \angle K \cong \angle M \) 2. (Reason: Given for \( \angle K \cong \angle M \)) 3. \( JL = LN \) 4. \( \angle KLJ \cong \angl…
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problem 6 how many solutions does this system of equations have? one so…
One solution (the option: One solution)
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problem 5 does this system of equations have a solution? yes no
Yes
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greg installed a circular drain that has a diameter of 4.8 inches. ques…
15.1
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problem 3 here are the graphs of those two lines. remember, a solution …
\((2,3)\) (corresponding to the option with \((2,3)\))
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39. fill in the missing statements and reasons to complete the followin…
1. Reason for Statement 1: Given 2. Reason for Statement 2: Definition of Bisector 3. Statement for Reason 3: \( \overline{BE} \cong \overline{ED} \) and \( \overline{AE} \cong \o…
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the wilson family’s back yard is a rectangular plot that has a length o…
A. 4400
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38. fill in the missing statements and reasons to complete the followin…
1. Reason for Statement 1: Given 2. Statement for Reason 2: $\overline{WY}$ bisects $\angle XWZ$ 3. Statement for Reason 3: $\angle XWY \cong \angle ZWY$ 4. Reason for Statement 4…
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determine the following. * 37. δrst is reflected to form δrst. select a…
A. $\overline{RT} \cong \overline{R'T'}$, E. $\angle R \cong \angle R'$
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find the measure of the arc whose length is given. 11. 12. 13.
For problem 11, 12, 13, the measure of the arc (central angle) is \( \boldsymbol{90^\circ} \) (or \( \frac{\pi}{2} \) radians) (depending on the given arc length and radius, but w…
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here is a square pyramid and its net. the lateral faces are congruent t…
(a) \( 25 \) \( \text{mm}^2 \) (b) \( 14.75 \) \( \text{mm}^2 \) (c) \( 59 \) \( \text{mm}^2 \) (d) \( 84 \) \( \text{mm}^2 \)
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4. angles a, d, and g are congruent, and angles c, f, and j are congrue…
# Explanation: ## Step1: Recall Triangle Angle Sum The sum of angles in a triangle is \(180^\circ\). For any triangle, \(\text{Sum of angles} = 180^\circ\). ## Step2: Apply to Eac…
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identify the vertex is (2 points) (1,5) (5,1) (4,0) (0,4) and is a mini…
The vertex is \((0,4)\) and it is a minimum. Wait, but the options: the first dropdown (vertex) has options (1,5), (5,1), (4,0), (0,4). The second dropdown is minimum/maximum. So …
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identify the \\( v \\) is it a maximum or minimum? options: (1,8) (5,1)…
The function (represented by the parabola) has a minimum.
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42. in the figure shown, δabc is a right triangle. \\(\\overline{bd}\\)…
18.5
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determine the following. * 43. in the diagram below, what is ac? diagra…
To determine the length of \( AC \), we use the Basic Proportionality Theorem (Thales' theorem), which states that if a line is drawn parallel to one side of a triangle, intersect…
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answer the following. when applicable, give the exact answer in terms o…
Length of \( \overarc{AB} \): \( 2\pi \) cm Length of \( \overarc{DE} \): \( \pi \) cm
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on your own . (mp) reason a graphic designer wants to reproduce a logo …
First, calculate the third angle (\(70^\circ\)) using the triangle angle - sum property. Then, draw a 2 - inch base. At each end of the base, draw \(60^\circ\) and \(50^\circ\) an…
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select the quotation from the story that most strongly suggests that th…
Alla was surprised by the structure and discipline involved in drawing a portrait.
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mirrors. others were working from photographs. alla glanced at the inco…
Don't assume you won't like something until you try it.
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(b) in the figure below, two chords intersect inside the circle at poin…
\( 20.25 \)
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(a) in the figure below, two secants are drawn to a circle from exterio…
\( \boxed{17} \)
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find n. right triangle with right angle at top left, horizontal leg lab…
\(10\)
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in the circle below, suppose m\\(\\overarc{kli}\\)=248° and m\\(\\angle…
(a) \(m\angle KLI = \boxed{56}\) degrees (b) \(m\angle LIJ = \boxed{49}\) degrees
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determine the following. * 52. find the coordinates of point p along th…
The coordinates of point \( P \) are \( (-1,\frac{1}{2}) \)
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in the circle below, ( overline{uw} ) is a diameter. suppose ( moverarc…
(a) \( \boldsymbol{28^\circ} \) (b) \( \boldsymbol{22^\circ} \)
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53. points d and n are on a number line. the expression \\(\\frac{4}{7}…
3: 4
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graph the inequality on a number line. 17. ( r leq -9 ) 18. ( g > 2.75 …
17. Closed circle at -9, shade left. 18. Open circle at 2.75, shade right. 19. Closed circle at -3.5, shade right. 20. Open circle at 1.25, shade left.
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the volume of this cone is 1,959.36 cubic millimeters. what is the radi…
\( 12.00 \)
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determine the following. * 54. which point on a number line is \\(\\fra…
10 (corresponding to the option "10")
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in the circle below, suppose m\\(\\overarc{wxu}\\) = 114° and m\\(\\ang…
(a) \(46^\circ\) (b) \(57^\circ\)
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read the passage. all through his boyhood and young manhood george will…
4. restlessness and contentment
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define perpendicular lines. a. lines that cut across two or more lines …
C. Two coplanar lines that intersect at a 90 - degree angle
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write an expression for the shaded region. 4x 3x + 5 x x + 2 (hint: fin…
\(a = 1\), \(b = 2\), \(c = 3\), \(d = 1\)
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solve for x and graph the solution on the number line below. -20 ≥ 10x …
Inequality Notation: \(x \leq -2\) (For the number line: Place a closed circle at \(-2\) and draw a line with an arrow pointing to the left from \(-2\) to cover all values less th…
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note: figure is not drawn to scale. if r = 5 units and x = 13 units, th…
B. 325π cubic units
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note: figure is not drawn to scale. if r = 5 units and x = 14 units, th…
A. 1,400π cubic units
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note: figure is not drawn to scale if the sphere shown above has a radi…
C. 523.33 cubic units
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write the coordinates of the vertices after a dilation with a scale fac…
\( D'(-8, -4) \) \( E'(8, -4) \) \( F'(-8, 4) \)
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note: figure is not drawn to scale. if r = 6 units and h = 8 units, wha…
A. 414.48 cubic units
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note: figure is not drawn to scale. if r = 6 units and h = 11 units, wh…
A. 640.56 cubic units
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5 charlie measured the circle - shaped part of a sun his sister drew on…
A. 22 cm
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two pairs of angles and two pairs of sides? how could we justify that △…
C. Side-angle-side congruence, D. Hypotenuse-leg congruence
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pairs of congruent corresponding angles must be similar. what does it m…
D. If we can map one figure onto the other using a sequence of rigid transformations and dilations, then the figures are similar.
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4 the diameter of the circle above is 20 cm. what is the circumference …
C. 62.8 cm
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10. (03.06 mc) the diagram below models the layout at a carnival where …
## Part A: A pair of similar triangles is \( \boldsymbol{\triangle GBC} \) and \( \boldsymbol{\triangle EBP} \) (or \( \triangle GCB \) and \( \triangle EPB \)). ## Part B: 1. Sin…
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note: figure is not drawn to scale. if n = 37 cm and l = 12 cm, what is…
A. 34 cm
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what is the volume of the card box? a. $8\\frac{3}{4}$ cu in b. $6\\fra…
D. $5\frac{5}{6}$ cu in
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find the distance between a and b. a. 4√7 units b. 11 units c. √14 unit…
D. $\sqrt{130}$ units
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3 the area of the circle above is 1,384.74 units². what is the circumfe…
D. 131.88 units
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note: figure is not drawn to scale. if k = 56 cm and l = 65 cm, what is…
A. 33 cm
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2\\frac{1}{6} ft\ ewline 1\\frac{1}{4} ft\ ewline *picture not drawn to…
assuming height is missing; correction: likely height is $4\frac{1}{3}=\frac{13}{3}$ from option B reverse check) ## Step2: Calculate volume $V=\frac{13}{6}×\frac{5}{4}×\frac{13}{…
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what is the perimeter of the isosceles triangle shown below? if necessa…
A. 24.98 units
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2. what are the domain and range? a domain: all real numbers range: y ≥…
A. Domain: all real numbers; Range: \(y\geq - 8\)
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find the distance between a and b. a. \\( \\sqrt{58} \\) units b. \\( 2…
A. $\sqrt{58}$ units
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which line has a slope of 8? line j line k line l line m line l line m …
None of these
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which line has a slope of \\(\\frac{2}{3}\\)? none of these line u line…
Line s