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 D C share common side A C. The lengths of A B and A D are congruent.

Question illustration
A
Yes, but only if AB ≅ DC.
B
Yes, but only if BC ≅ DC.
C
No, because AB is not congruent to AC.
D
No, because AB ≅ DA.
2
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△ABC is an isosceles triangle with legs AB and AC. △AYX is also an isosceles triangle with legs AY and AX.

Question illustration
A
∠A ≅ ∠A; reflexive property
B
∠X ≅ ∠X; reflexive property
C
∠ABC ≅ ∠AYX; corresponding angles of similar triangles
D
∠ABC ≅ ∠AXY; corresponding angles of similar triangles
3

Triangles D E F and D prime E prime F prime are connected at point E. Triangle D E F is rotated about point E to form triangle D prime E prime F prime.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
4

Triangle J K L is shown. Angle J K L is a right angle. An altitude is drawn from point K to point M on side L J to form a right angle.

Question illustration
A
ΔJKM
B
ΔMKL
C
ΔKML
D
ΔLJK
5

The statements below can be used to prove that the triangles are similar. ? △ABC ~ △XYZ by the SSS similarity theorem.Which mathematical statement is missing?

Question illustration
A
StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction
Option A
B
∠B ≅ ∠Y
C
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
Option C
D
∠B ≅ ∠Z
6

In the diagram, .

Question illustration
A
WV and XY
B
WV and ZY
C
∠VZW ≅ ∠YZX
D
∠VWZ ≅ ∠YXZ
7

Triangles W X Z and Y Z X share common side X Z. Angles W X Z and X Z Y are right angles. The lengths of sides W X and Z Y are 21 centimeters.

Question illustration
A
Yes, they are congruent by SAS.
B
Yes, they are both right triangles.
C
No, the triangles share side XZ.
D
No, there is only one set of congruent sides.
8

Which statements are correct? Select three options.

A
△BCD is similar to △BSR.
B
StartFraction B R Over R D EndFraction = StartFraction B S Over S C EndFraction
Option B
C
If the ratio of BR to BD is , then it is possible that BS = 6 and BC = 3.
Option C
D
(BR)(SC) = (RD)(BS)
E
StartFraction B R Over R S EndFraction = StartFraction B S Over S C EndFraction
Option E
9

Read the proof.Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°Prove: △HKJ ~ △LNP

Question illustration
A
CPCTC
B
definition of supplementary angles
C
triangle parts relationship theorem
D
triangle angle sum theorem
10

Triangles A B C and A double-prime B double-prime C double-prime are shown. Triangle A double-prime B double-prime C double-prime is smaller and to the right of triangle A B C.

Question illustration
A
a reflection and a dilation
B
a rotation and a dilation
C
a translation and a dilation
D
a reflection and a translation
11

Triangles A B C and A B F are congruent. Triangle A B C is reflected across line B A to form triangle A B F.

Question illustration
A
a rotation about point A
B
a reflection across the line containing CB
C
a reflection across the line containing BA
D
a rotation about point B
12

Triangles A B C and N M Q are shown. Sides B C and N M are congruent. Angles A B C and Q N M are congruent. Angles B C A and N M Q are both right angles.

Question illustration
A
A ≅ Q because of the third angle theorem.
Option A
B
AB ≅ QN because they are both opposite a right angle.
C
BC ≅ NM because it is given.
D
C ≅ M because right angles are congruent.
Option D
13

To prove that ΔAED ˜ ΔACB by SAS, Jose shows that .

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

Which pair of triangles can be proven congruent by SAS?

A
2 triangles with identical angle measures are shown. The second triangle is shifted to the right.
Option A
B
2 triangles are shown. They have 2 congruent sides and a congruent angle. The first triangle is rotated about a point to form the second triangle.
Option B
C
2 triangles are shown. They have 1 congruent side and 2 congruent angles. The first triangle is rotated about a shared side to form the second triangle.
Option C
D
Option
Option D
15

How can ΔABC be mapped to ΔXYZ?

Question illustration
A
vertex B to vertex Z
B
vertex B to vertex Y
C
vertex A to vertex Z
D
vertex A to vertex Y

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