Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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on a coordinate plane, point b(-6, 1) is translated to b(-3, -2). indir…
The translation rule is \((x,y)\to(x + 4,y - 4)\) (or \((x,y)\to(x + 4,y+(-4))\))
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which rule can be used to describe the x - coordinates in the translati…
\( x + 0 \) (the first option, assuming the options are: \( x + 0 \), \( x + 6 \), \( x - 6 \), etc. So the correct rule for \( x \)-coordinates is \( x + 0 \).
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which triangle is a translation of triangle p? graph of coordinate plan…
triangle B
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point a(7, 3) is translated to a(18,-9). which rule describes the trans…
\((x,y)\to(x + 9,y - 12)\) (the last option: \((x,y)\to(x + 9,y - 12)\))
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the triangle on the grid will be translated two units left. which shows…
To solve the problem of translating the triangle two units left, we follow these steps: ### Step 1: Identify the coordinates of the original triangle's vertices First, we determin…
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if the triangle on the grid below is translated by using the rule ((x,y…
\((-4, 0)\)
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which rule describes the translation below? graph of two right triangle…
\((x,y)\to(x - 5,y - 3)\)
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2. what is the solution to the following system of equations? options: …
O (1, -3)
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john says the transformation rule (x, y) → (x + 4, y + 7) can be used t…
John used the transformation rule \((x,y)\to(x + 4,y + 7)\) (adding 4 to the x - coordinate and 7 to the y - coordinate) instead of the correct rule \((x,y)\to(x - 4,y - 7)\) (sub…
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if $qr = 8$, $rs = 12$, and $uv = 14$, find the length of $overline{tu}…
$9.3$
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in this figure, what is the value of x if y = 38°? triangle with angles…
$90^\circ$ *(Note: The provided options do not include the correct calculated value. The correct value of $x$ is 90 degrees.)*
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in triangle pqr, shown below, angle p measures 140°. angle q has the sa…
$20^\circ$
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what is the measure of angle r? (there is a triangle rqs with angle at …
A. 17 degree
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the measure of the vertex angle of an isosceles triangle is 50. find th…
$65^\circ$
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the measure of the vertex angle of an isosceles triangle is 70. find th…
$55^\circ$
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62 the lengths of the sides of a triangle are 8, 15, and 17. if the lon…
B. 24
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61 which set of numbers could represent the lengths of the sides of a t…
A. 9,16,20
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60 which set of numbers could represent the lengths of the sides of a t…
A. 6,8,9
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analyzing student work john says the transformation rule (x, y) → (x + …
John's error was that he used the transformation rule \((x,y)\to(x + 4,y + 7)\) (adding 4 to the \(x\) - coordinate and 7 to the \(y\) - coordinate) instead of the correct rule \(…
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segment pl has endpoints p(4, -6) and l(-2, 1). the segment is translat…
P'(9, -6), L'(3, 1) (the third option: P'(9, -6), L'(3, 1))
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which set of numbers can not represent the lengths of the sides of a tr…
C. 7,18,11
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if the triangle and the rectangle have the same area, what is the value…
B. 3
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what is the area of δabc if ad = 20, ab = 25, and cd = 9?
240
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the area of the rectangle is 270 km². what is the area of the shaded tr…
B. $135\ \text{km}^2$
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writing a translation rule a triangle has coordinates f(-2, 3), g(-4, 1…
The correct option is the second one: \( \boldsymbol{(x, y) \to (x + 2, y - 3)} \) (corresponding to the option labeled as the second choice, e.g., if options are A to D, assuming…
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a figure is translated using the mapping $(x, y) \\to (x + a, y + b)$. …
The figure moves left and down.
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a figure is translated using the rule (x, y) → (x − 3, y + 6). which de…
left 3 units and up 6 units (the last option: left 3 units and up 6 units)
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a triangle has sides with lengths of 59 yards, 75 yards, and 50 yards. …
no
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a triangle has sides with lengths of 16 inches, 63 inches, and 65 inche…
yes
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a triangle has sides with lengths of 83 meters, 96 meters, and 58 meter…
no
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part 2 of 2 estimation without doing calculations, use side de and side…
$\frac{7}{2}$
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the point p(6, -1) is translated according to the rule (x, y) → (x - 5,…
\(P'(1, - 3)\) (which corresponds to the option \(P'(1,-3)\))
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estimation without doing calculations, use side de and side de to estim…
$\frac{5}{2}$
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triangle abc has vertices a(4, 5), b(0, 5), and c(3, -1). the triangle …
\((-3, 6)\)
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translating a figure triangle abc has vertices a(4, 5), b(0, 5), and c(…
\((-3, 6)\) (corresponding to the option \((-3, 6)\))
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triangle abc is translated 6 units to the right and 1 units up. what ar…
A. \(C'(4, - 2)\)
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which are true statements about a translation? select all that apply. □…
- The image is congruent to the pre - image. - The image could be moved left or right. - The image could be moved up or down.
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practice identifying translations on a plane. the translation shown in …
The translation shown is a horizontal translation (or a translation of 6 units to the right, but since the question says "what kind of", likely horizontal translation as it moves …
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finding the translation rule triangle def has coordinates d(-3, -2), e(…
\( (x,y) ightarrow(x + 4,y - 2) \) (the fourth option, i.e., the option with \( (x,y) ightarrow(x + 4,y - 2) \))
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question 9 assume the two trapezoids are similar. what is the value of …
x = 5.5? Correction: Correct pair: lower trapezoid's bottom side (unknown, but upper trapezoid's bottom is 20, lower trapezoid's vertical side 24 corresponds to upper's 25, so sca…
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question 8 2 points find the measure of angle m based on the shape belo…
96° (Option C: 96°)
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identify the rule for the transformation shown in the figure that trans…
\( (x, y) \to (x + 4, y + 2) \) (the last option)
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find the number of sides of the regular polygon where the sum of the in…
1. 16-gon 2. A 40-gon 3. 64° and 96°
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for what value of x will make the two triangles similar? image of two t…
x = 10.2 --- ### Second Problem (Quadrilateral Angles)
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solve for x given the following similar triangles. image of two similar…
x = 8
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question 1 are the following triangles similar? image of two triangles …
No, they are not similar
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question 5 1 point gabe said that the interior angles of any pentagon a…
Gabe is incorrect because only regular pentagons would have this property, not any pentagon.
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question 2 1 point which method would not result in the correct answer …
Cross-multiplying $\frac{108.5}{31} = \frac{x}{42}$ would not result in the correct answer. The first ratio has the taller tree's height over its shadow length, but the second rat…
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307 < 11b + 32 < 318 progress: 1/3 part 2 of 3 (b) the solution set for…
The solution to the compound inequality \( 307 < 11b + 32 < 318 \) is \( 25 < b < 26 \). On the number line, this would be represented by an open circle at 25 and an open circle a…
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translations- a transformation in which each point of a figure moves th…
### Part 1: Filling in the Blanks about Translations #### Explanation for Translations Definition: A translation is a transformation where each point of a figure moves the same **…
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which angles are complementary to ∠1? select all that apply. ∠4 ∠5 ∠6 ∠2
$\angle 4$, $\angle 6$
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which angles are adjacent to each other? select all that apply. ∠4 and …
- $\angle4$ and $\angle3$ - $\angle1$ and $\angle5$
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which angles are adjacent to ∠7? select all that apply. ∠6 ∠8 ∠3 ∠5
A. $\angle 6$ B. $\angle 8$ D. $\angle 5$
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which angles are adjacent to each other? ∠2 and ∠5 ∠1 and ∠3 ∠4 and ∠2 …
$\angle1$ and $\angle2$
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which angles are vertical to each other? select all that apply. ∠11 and…
$\boldsymbol{\angle5}$ and $\boldsymbol{\angle7}$, $\boldsymbol{\angle4}$ and $\boldsymbol{\angle2}$
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write the coordinates of the vertices after a translation 8 units left …
\( P'(-6, -11) \) \( Q'(-2, -11) \) \( R'(-10, -4) \)
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write the coordinates of the vertices after a translation 3 units right…
\( E'(-2,-8) \), \( F'(-2,-3) \), \( G'(4,-3) \), \( H'(4,-8) \)
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question 10 △ abc ~△ qrs c = 37.8; s = 14.8; q = 9; b = 19 what is r? h…
\(7.44\)
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question 1 2 pts image of a right triangle with legs a, b and hypotenus…
38.08
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lake quiz exit = ge question 9 2 pts △abc ~△qrs c = 21.7; s = 11.3; q =…
\( 11.52 \)
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question 6 (multiple choice worth 5 points) (07.03 mc) the figure below…
125.6 feet (the option with 125.6 feet)
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the triangle ace, is a dilation image of triangle abd. point a is the c…
1. The dilation is an enlargement. 2. The scale factor of the dilation is $\frac{4}{3}$
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question 4(multiple choice worth 5 points) (07.03 mc) a circular walkin…
A. Center at \((-3, 4)\); \(r = 8\)
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two parallel lines are cut by a transversal as shown below. suppose $m\…
\( m\angle2 = \boldsymbol{79}^\circ \) \( m\angle3 = \boldsymbol{101}^\circ \)
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the blue figure is a dilation image of the black figure. the labeled po…
- Dilation type: Reduction - Scale factor: $\frac{1}{3}$
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two parallel lines are cut by a transversal as shown below. suppose ( m…
\( m\angle 2 = 79^\circ \), \( m\angle 3 = 101^\circ \)
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two parallel lines are cut by a transversal as shown below. suppose $m\…
\( m\angle 2 = \boxed{37}^\circ \) \( m\angle 3 = \boxed{143}^\circ \)
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two parallel lines are cut by a transversal as shown below. suppose m ∠…
\(m\angle5=\boldsymbol{52}^{\circ}\), \(m\angle7=\boldsymbol{52}^{\circ}\)
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give one pair of supplementary angles and one pair of vertical angles s…
(a) Supplementary angles: \(\angle1\) and \(\angle2\) (or any linear pair, e.g., \(\angle3\) and \(\angle4\), etc.) (b) Vertical angles: \(\angle2\) and \(\angle6\) (or \(\angle1\…
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question 1 (multiple choice worth 5 points) (07.02 mc) quadrilateral op…
A. \((6x - 4)^\circ + (2x + 16)^\circ = 180^\circ\)
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in the figure below, $m\\angle 4 = 96^{\\circ}$. find $m\\angle 1$, $m\…
\( m\angle1 = \boxed{84}^\circ \) \( m\angle2 = \boxed{96}^\circ \) \( m\angle3 = \boxed{84}^\circ \)
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in the figure below, $m\\angle 1 = 71^{\\circ}$. find $m\\angle 2$, $m\…
\( m\angle2 = \boldsymbol{109}^\circ \) \( m\angle3 = \boldsymbol{71}^\circ \) \( m\angle4 = \boldsymbol{109}^\circ \)
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find the value of x. (there is a triangle and a straight line forming a…
\(x = 52\)
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find the value of x. triangle with 35° angle at top, x° angle at bottom…
\(x = 85\)
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find the value of x.
\(131^\circ\)
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find the value of x. triangle with angles 38°, 76°, and x°
$66$
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2 tries left. please try again. select the angle(s) with measures that …
C) $\angle 4$, D) $\angle 7$, F) $\angle 1$
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what is the measure of angle qpr in the given figure? (figure with a ci…
A. 32°
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select the correct answer. points a, b, and c are located on a circle, …
C. 176°
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select the correct answer from each drop - down menu. three students ar…
The student with the correct approach is Jordan; The diameter of the circle is 75 units.
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select the correct answer from each drop-down menu. three students are …
Jordan; 63
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select the correct answer (overleftrightarrow{dg}) and (overleftrightar…
B. 140°
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question 6 of 10 which of the following is most likely the next step in…
D. (The circle with a diameter, two points on the circumference and the center in between)
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for the set of triangle vertices, find the coordinates of the vertices …
\( J'(-3, 2) \), \( K'(1, 0) \), \( L'(-3, -2) \)
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write the coordinates of the vertices after a translation 7 units left.…
$B'(-5, 2)$ $C'(-5, 7)$ $D'(0, 7)$ $E'(0, 2)$
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given the two rectangles below. find the area of the shaded region. 4 2…
34
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solve for x and graph the solution on the number line below. if possibl…
Inequality Notation: $8 < x \leq 10$ For the number line: - Draw an open circle at 8, a closed circle at 10, and shade the region between 8 and 10 (including 10, excluding 8).
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solve for x and graph the solution on the number line below. if possibl…
Inequality Notation: $8 < x \leq 10$ For the number line: - Draw an open circle at 8 (since $x > 8$ does not include 8) and a closed circle at 10 (since $x \leq 10$ includes 10). …
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solve for x and graph the solution on the number line below. if possibl…
Inequality Notation: $x \leq 9$ For the number line: Draw a closed circle at 9, and shade all values to the left of 9 (including 9) to represent all real numbers less than or equa…
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graph the set {x | 3 < x < 6} on the number line. then, write the set u…
Graph: Open circles at 3 and 6, shaded region between them. Interval notation: $(3,6)$
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the actual lengths of the garden are shown in the table. choose an equi…
The equivalent ratio is \( 1 \text{ in} : 4 \text{ ft} \) (or \( 6:24 = 1:4 \) when simplified).
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question solve for x and graph the solution on the number line below. i…
Inequality Notation: $x \geq 6$ For the number line: Plot a closed circle at 6, and draw a line extending to the right (towards positive infinity).
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name the quadrant or axis where each point lies. (-6, 3): (choose one) …
(-6, 3): Quadrant II (-5, -6): Quadrant III (6, 0): x-axis (2, 4): Quadrant I
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find the area and the circumference of a circle with radius 9 yd. use t…
Area: $254.34$ yd² Circumference: $56.52$ yd
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a circle with center g is shown in the figure below. (a) name a diamete…
(a) $\overline{HK}$ (b) $\overline{GF}$ (c) $\overline{JI}$ (d) 5 units
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question find the distance between the two points in simplest radical f…
13
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when publicity stunts get goofy teen channel: business theres a red car…
C. ways that companies market their products
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use pascals triangle to expand ((y^2 + z^2)^3). express your answer in …
\(y^{6}+3y^{4}z^{2}+3y^{2}z^{4}+z^{6}\)
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determine whether the pair of figures is similar. if so, find the scale…
The pair of triangles is not similar because their corresponding angles are not equal (the angle measures of the two triangles do not match the requirements of the AA similarity c…
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find the slope of the line that passes through these two points. (2, -3…
Slope: $\frac{7}{4}$ a) positive