AnswersGA-Geometry Concepts and Connections A-CRRight Triangle Similarity

Right Triangle Similarity — Cumulative exam Answers

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1
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is an altitude in triangle WXZ.

Question illustration
A
XWZ is an obtuse angle.
Option A
B
XWZ is a right angle.
Option B
C
XWZ is congruent to WXY.
Option C
D
XWZ is congruent to XZW.
Option D
2
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and are midsegments of ΔWXY.

Question illustration
A
11.57 cm
B
12.22 cm
C
12.46 cm
D
14.50 cm
3

Which best explains why all equilateral triangles are similar?

A
All equilateral triangles can be mapped onto each other using dilations.
B
All equilateral triangles can be mapped onto each other using rigid transformations.
C
All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D
All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.
4

Question text not available

Question illustration
A
3 ft
B
4 ft
C
18 ft
D
12 ft
5

Read the proof.Given: AB ∥ DEProve: △ACB ~ △DCE

Question illustration
A
AA similarity theorem.
B
SSS similarity theorem.
C
AAS similarity theorem.
D
ASA similarity theorem.
6

On a coordinate plane, a line is drawn from point A to point B. Point A is at (9, negative 8) and point B is at (negative 6, 7).

Question illustration
A
(2, –1)
B
(4, –3)
C
(–1, 2)
D
(3, –2)
7

Quadrilateral JKLM was dilated according to the ruleDO,(x,y) to create the image quadrilateral J'K'L'M', which is shown on the graph.

Question illustration
A
(0, -4)
B
(0, -1)
C
(0, 0)
D
(0, 4)
8

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20.

Question illustration
A
9 units
B
12 units
C
15 units
D
18 units
9

On a number line, the directed line segment from Q to S has endpoints Q at –14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio.Which expression correctly uses the formula to find the location of point R?

Question illustration
A
(StartFraction 3 Over 3 + 5 EndFraction) (2 minus (negative 14)) + (negative 14)
Option A
B
(StartFraction 3 Over 3 + 5 EndFraction) (negative 14 minus 2) + 2
Option B
C
(StartFraction 3 Over 3 + 5 EndFraction) (2 minus 14) + 14
Option C
D
StartFraction 3 Over 3 + 5 EndFraction (negative 14 minus 2) minus 2
Option D
10

On a coordinate plane, Rectangles A B C D and E F G H are shown. The length of side A B is 6 units and the length of side B C is 3 units. The length of side E F is 8 units and the length of side F G is 4 units.

Question illustration
A
Yes, because corresponding sides are parallel and have lengths in the ratio
Option A
B
Yes, because both figures are rectangles and all rectangles are similar.
C
No, because the center of dilation is not at (0, 0).
D
No, because corresponding sides have different slopes.
11

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3.

Question illustration
A
∠DFE is 4 times greater than ∠GFH.
B
∠FHG is the measure of ∠FED.
Option B
C
∠DFE is congruent to ∠GFH.
D
∠FHG is congruent to ∠EFD.
12

Triangle RST was dilated by a scale factor of . The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units.

Question illustration
A
4 units
B
8 units
C
16 units
D
20 units
13

Consider the two triangles.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
14

Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5.

Question illustration
A
Yes, it is an enlargement with a scale factor of 3.
B
Yes, it is an enlargement with a scale factor of .
Option B
C
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
D
No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
15

Triangle N T M is shown. Angle N T M is a right angle. An altitude is drawn from point T to point U on side N M to form a right angle. The length of N T is y, the length of T M is 6, the length of N U is 9, and the length of U M is 3.

Question illustration
A
units
Option A
B
units
Option B
C
units
Option C
D
units
Option D
16

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of R T is x.

Question illustration
A
12 units
B
15 units
C
20 units
D
25 units
17

Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'.

Question illustration
A
One-eighth
Option A
B
One-fourth
Option B
C
4
D
8
18

Triangle TVW is dilated according to the ruleDO,(x,y) to create the image triangle T'V'W', which is not shown.

Question illustration
A
T'(-3, 6) and V'(0, 3)
B
T'(-3, 6) and V'(0, 1)
C
T'(-1, 2) and V'(0, 3)
D
T'(-1, 2) and V'(0, 1)
19

Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6.

Question illustration
A
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U
Option A
B
StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction
Option B
C
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U
Option C
D
StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Option D
20

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

A
0.1
B
Option
Option B
C
1
D
10

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