Geometry
Triangles, circles, coordinate geometry, and proof-oriented questions.
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are the vectors orthogonal?\ \\langle 3, 2\ angle, \\langle -6, 18\ ang…
No
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solve for x. figures are not necessarily drawn to scale.
$27$
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use the figure to find the specified vector. find a - b. graph of vecto…
B. \(\langle11,3 angle\)
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solve for ( x ). figures are not necessarily drawn to scale. (image of …
\( x = 13.2 \)
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question solve for ( x ). figures are not necessarily drawn to scale. (…
$x = 7.2$
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find the area of triangle abc with the given parts. round to the neares…
D. \(107\space cm^{2}\)
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solve for x. figures are not necessarily drawn to scale. answer attempt…
$x = 8$? Wait, no, wait, I think I made a mistake. Wait, maybe the sides are $FH = 6$, $HE = 4.8$, so $FE=FH + HE=10.8$? No, wait, maybe the correct proportion is $\frac{FH}{FD}=\…
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find the missing parts of the triangle. (find angles to the nearest hun…
A. \(A = 21.12^{\circ}, B = 24.43^{\circ}, C = 134.45^{\circ}\)
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find the length of side a. a triangle abc with angle at a being 45 degr…
D. \(\sqrt{13}\)
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7 practice 7 (from unit 4, lesson 1) a step has a height of 6 inches. a…
B. The angle would increase.
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determine the number of triangles abc possible with the given parts. a …
C. 0
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6 practice 6 (from unit 4, lesson 2) what is the length of the square’s…
B. \(\frac{6}{\sqrt{2}}\) units
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current skill $ what is the value of x?
\(25\)
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find the missing parts of the triangle. round angles to one decimal pla…
C. No such triangle exists
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4 practice 4 (from unit 4, lesson 3) triangle abc, shown here, is equil…
a. \(x = 4\sqrt{3}\) b. \(60\)
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find the measures of all the angles in the rectangle.
\( \angle 1 = 90^\circ \), \( \angle 2 = 68^\circ \), \( \angle 3 = 90^\circ \), \( \angle 4 = 90^\circ \), \( \angle 5 = 22^\circ \)
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what is the value of x? (with a diagram of intersecting lines and angle…
\(x = 25\)
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current skill $ find the measure of angle 4. label optional
\(64^\circ\)
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3 practice 3 priya says, \i know everything about a right triangle with…
Missing angles: \(60\) and \(90\) Missing side lengths: \(1\) and \(1.732\)
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2 practice 2 here is triangle abc. estimate the values to complete the …
| angle | adjacent leg ÷ hypotenuse | opposite leg ÷ hypotenuse | opposite leg ÷ adjacent leg | | --- | --- | --- | --- | | \(A\) | \(0.26\) | \(0.97\) | \(3.70\) |
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find the slope and y-intercept. slope: y-intercept:
slope: \(3\) y - intercept: \(2\)
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sophie wants to lay carpeting over a certain area of her apartment. par…
Expression: \( x^2 - 4 \) (assuming \( x \) is the side of large square), and if \( x \) is, say, 10, evaluated is 96 (but need \( x \) value). Wait, maybe the original problem ha…
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current skill find the measure of angle 2. label optional
\(103^\circ\)
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use the image below to find the requested values. find the measure of ∠…
35°
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10. q is equidistant from the sides of ∠tsr. find the value of x. (2x +…
3
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9. look at the figure. find the value of x. figure of a quadrilateral w…
12
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find the measure of the missing angle. 97° label optional
\(83^\circ\)
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7. how many solutions are there to the graph below?
1
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4. look at the figure. find the value of cg. (figure with segments labe…
8
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find the measure of ∠q in parallelogram qrst. t q 5x + 12 3x + 46 s r l…
\(97^\circ\)
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aisha is trying to determine if △lmn and △pqr are similar, congruent, o…
The triangles are similar by the SSS similarity theorem.
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3. look at the figure. find jm. figure of a quadrilateral with right an…
17 (the last option, with identifier and text: the option with 17)
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abcd is a parallelogram. find the length of \\(\\overline{ad}\\). a 9y …
The length of \(\overline{AD}\) is \( 2 \).
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in the diagram, ab is 6 units, bc is 30 units, and ae is 4 units. if δa…
24 units (corresponding to the option "24 units")
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what is the value of x?
\(15\)
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consider the two triangles. how can the triangles be proven similar by …
Show that the ratios \(\frac{XZ}{WU}\) and \(\frac{ZY}{WV}\) are equivalent, and \(\angle U\cong\angle Z\) (the fourth option: "Show that the ratios \(\frac{XZ}{WU}\) and \(\frac{…
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below are statements that can be used to prove that the triangles are s…
The correct option (assuming the option is structured as: \(\angle B\cong\angle Y\) and \(\triangle ABC\sim\triangle ZYX\) by the SAS similarity theorem) – but based on the given …
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in the diagram, \\(\\frac{sq}{om} = \\frac{sr}{on} = 4\\). to prove tha…
\(\overline{MN}\) and \(\overline{QR}\) (the second option)
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which would prove that δabc ~ δxyz? select two options. □ \\(\frac{ba}{…
The two options that prove \(\triangle ABC \sim \triangle XYZ\) are: 1. \(\boldsymbol{\frac{BA}{YX}=\frac{BC}{YZ}=\frac{AC}{XZ}}\) 2. \(\boldsymbol{\frac{AC}{XZ}=\frac{BA}{YX},\an…
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what value of x will make △onm similar to △srq by the sas similarity th…
25
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which diagram(s) show triangles that we can prove are similar using the…
# Explanation: ## Step1: Recall AA Similarity Criterion The Angle - Angle (AA) similarity criterion states that if two angles of one triangle are congruent to two angles of anothe…
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current skill $\ $what is the value of x?\
17
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below are statements that can be used to prove that the triangles are s…
The correct option is the first one: \(\boldsymbol{\angle X \cong \angle C}\) and \(\boldsymbol{\triangle ABC \sim \triangle ZYX}\) by the SAS similarity theorem.
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aph the parabola. y=(x+1)^2+5 plot five points on the parabola: the ver…
The five points on the parabola \( y=(x + 1)^2+5 \) are: Vertex \((-1, 5)\), left points \((-3, 9)\), \((-2, 6)\), right points \((0, 6)\), \((1, 9)\).
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four pairs of triangles are shown below. select the pair(s) that provid…
The pairs are the first (green), second (purple), and fourth (blue) pairs? Wait, recheck fourth: first blue has \(30^\circ\), second blue has \(30^\circ\), \(99^\circ\), \(51^\cir…
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find the radius (to the nearest hundredth of a millimeter) of a pulley …
A. 22.10 mm
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two similar triangles are shown. fill in the missing angle measure and …
Missing angle (larger triangle): \(47^\circ\) Missing side (smaller triangle): \(7.5\) cm
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all of the quadrilaterals in the shape below are squares. find the area…
# Explanation: ## Step1: Determine the side length of the large square The large square's side length is the sum of the side lengths of the two smaller squares? Wait, no. Wait, lo…
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triangle fgh and triangle klm are shown below. the measure of ∠h is equ…
Showing that $\boldsymbol{\angle F=\angle K}$ would prove the triangles are similar based on the $\boldsymbol{\text{angle - angle (AA) criterion}}$.
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triangle fgh and triangle klm are shown below. the measure of ∠h is equ…
First drop - down: angle F = angle K; Second drop - down: AA (Angle - Angle) Similarity
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triangle fgh and triangle klm are shown below. the measure of ∠h is equ…
First drop - down: \(\boldsymbol{\angle G=\angle L}\) (or \(\boldsymbol{\angle F=\angle K}\)) Second drop - down: \(\boldsymbol{AA}\) (Angle - Angle) Similarity Criterion
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note: figure not drawn to scale. the circle shown has center o, circumf…
B) \( 48\pi \)
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surface area & volume what is the volume of the prism shown below? (pri…
\( 84 \)
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this is her design, using one rectangular prism and two parallelogram p…
24 cubic inches
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kathy is designing a \k\ for her bedroom door. she wants to buy wood fr…
24 cubic inches (the option with "24 cubic inches")
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max is building a model of a hotel that he is designing for a client. w…
330
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a square pyramid is shown below. image of a square pyramid with base ed…
\( 64 \)
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what is the surface area of the rectangular prism shown below? image of…
94
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what is the measure of angle z? 26° w y 121° z 85° 95° 121° 52°
\( 95^\circ \)
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4. what is m∠lkh? options: 50, 80, 40, 25
40 (the option with 40, so the third option: 40)
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what is the value of y? 99° 45° degrees
\(36\)
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for the triangle below, what is the measure of the exterior angle shown…
\(130\)
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pujah drew a triangle with angle measures 76, 24, and x. what must be t…
80
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what is the measure of angle z? 124° 71° degrees
\(53\)
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anula is making a scale model of her kitchen table for her dollhouse. t…
14
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the two trapezoids shown below are similar. what is the value of x? x =…
$\frac{5}{2}$ (or $2\frac{1}{2}$)
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two similar triangles are shown below. fill in the missing side length …
27
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squares stuv and wxyz are similar. the ratio of the side lengths of squ…
\( 21 \)
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part of the net of a rectangular prism is shown. use the polygon tool t…
To draw the missing faces: 1. For the top - left missing face: Connect the top - right corner of the top - left rectangle (from the given net) horizontally to the right (same leng…
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what shapes make up the net of a hexagonal prism? use the drop - down m…
2 Hexagons and 6 Rectangles (or in the context of the drop - down, the first shape type is "Hexagon" (with quantity 2 implied by the prism's base count) and the second is "Rectang…
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which line segment shows the height that corresponds to the given base …
B. \( B \)
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what three - dimensional figure has a total of 4 surfaces (the sum of t…
triangular pyramid (or tetrahedron)
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nets of 3-d shapes what is the shape of the base in a cone? the base is…
circle
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which shape(s) could have this figure as a base? image of a right trian…
A. pyramid, D. prism
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find the value of x. (there is a quadrilateral with angles 94°, 86°, 49…
\(131\)
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find the value of x. (there is a quadrilateral with angles 50°, 109°, 1…
\(100\)
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for what value of x is g(x) = -2?
\( x=-4 \)
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use the graph of g to find g(8). g(8) = \\square
\( g(8)=-3 \)
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victor’s storage space is shown in the image below. what is the area of…
28
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which line segment shows the base that corresponds to the given height …
A. \(A\)
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a cube with faces of different colors is shown. all three of the hidden…
The leftmost square in the middle row (middle row, first square)
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what three - dimensional figure has a total of 5 surfaces (the sum of t…
The first dropdown: A(n) **triangular** (selected). The second dropdown: **prism** (to complete "triangular prism", which has 5 surfaces).
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what three-dimensional figure has a total of 5 surfaces (the sum of the…
First dropdown: triangular, Second dropdown: prism (or First dropdown: square, Second dropdown: pyramid)
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match the base to the corresponding height. base (b) | height (h) trian…
- Top - left base \( b \) ↔ Top - right height \( h \) - Middle - left base \( b \) ↔ Middle - right height \( h \) - Bottom - left base \( b \) ↔ Bottom - right height \( h \)
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current skill what is the value of x?
\(12\)
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which line segment shows the height that corresponds to the given base …
B
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use the vertical line test to determine if y is a function of x in the …
y is not a function of x
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brookes swimming pool is shown in the image below. what is the area of …
90 m²
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use the vertical line test to determine if y is a function of x in the …
A. \( y \) is a function of \( x \)
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match the base to the corresponding height. base (b) | height (h) (imag…
- First base (red \(b\)) matches the height triangle with the right - angled mark at the base of \(h\) (top - right height triangle). - Second base (horizontal \(b\)) matches the …
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current skill $\\$ find the measure of angle 6.
The measure of angle 6 is \(\boldsymbol{70}\) degrees.
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arthur is drawing the faces of a rectangular prism so that he can make …
The two missing faces to drag are the third and fourth faces (from the left) in the "Missing Faces" row (the ones with 3 columns and 4 rows of squares).
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which line segment shows the base that corresponds to the give of the t…
B. B
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which line segment shows the base that corresponds to the given height …
A (the line segment labeled \( A \))
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current skill $ 8x + 68 2 3 4 5 -6x + 116 7 8 find the measure of angle…
The measure of angle 2 is \(\boldsymbol{128}\) degrees.
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question 13 score: 0 of 1 point find the distance between (-18, 3) and …
\(\sqrt{785}\)
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the parallelogram shown below has an area of 84 units². find the missin…
14
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the parallelogram shown below has an area of 24 units². find the missin…
\( 4 \)
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the parallelogram shown below has an area of 72 units². find the missin…
12
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arthur is drawing the faces of a rectangular prism so that he can make …
The two missing faces are the second (the middle - small) face in the "Missing Faces" row (and its congruent copy, but since we need to drag two, we select the two faces with dime…