AnswersGA-Geometry Concepts and Connections A-CRRight Triangle Similarity

Right Triangle Similarity — Unit test Answers

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Triangles A B C and A double-prime B double-prime C double-prime connect at point C. Triangle A B C is rotated and then made smaller to form triangle A double-prime B double-prime C double-prime.

Question illustration
A
a rotation and a reflection
B
a translation and a dilation
C
a reflection and a dilation
D
a dilation and a rotation
2
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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
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

Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

Question illustration
A
16
B
24
C
32
D
36
5

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
6

and are midsegments of ΔWXY.

Question illustration
A
11.57 cm
B
12.22 cm
C
12.46 cm
D
14.50 cm
7

Consider the two triangles.

Question illustration
A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
8

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
9

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
10

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.
11

Consider △RST and △RYX.

Question illustration
A
StartFraction R Y Over Y S EndFraction = StartFraction R X Over X T EndFraction = StartFraction X Y Over T S EndFraction
Option A
B
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction
Option B
C
StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction R S Over R Y EndFraction
Option C
D
StartFraction R Y Over R X EndFraction = StartFraction R S Over R T EndFraction = StartFraction X Y Over T S EndFraction
Option D
12

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
13

Triangle R Q S is cut by line segment T V. Line segment T V goes from side Q R to side R S. The length of R V is x + 10, the length of V S is x, the length of R T is x + 4, and the length of T Q is x minus 3.

Question illustration
A
3
B
8
C
10
D
11
14

Triangles L M N and P O N connect at point N. Angles L M N and N O P are congruent.

Question illustration
A
because both triangles appear to be equilateral
B
because∠MNL and ∠ONP are congruent angles
C
because one pair of congruent corresponding angles is sufficient to determine similar triangles
D
because both triangles appear to be isosceles, ∠MLN ≅ ∠LMN, and ∠NOP ≅ ∠OPN
15

Question text not available

Question illustration
A
3 ft
B
4 ft
C
18 ft
D
12 ft
16

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.
17

Points J and K are midpoints of the sides of triangle FGH.

Question illustration
A
2
B
5
C
7
D
8
18

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 S R is x.

Question illustration
A
12 units
B
15 units
C
20 units
D
24 units

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