AnswersPMHS Geometry Q2Using Triangle Congruence Theorems

Using Triangle Congruence Theorems — Unit test Answers

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21
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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.
22
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On a coordinate plane, 2 triangles are shown. Triangle A B C has points (negative 1, negative 1), (2, negative 1), and (negative 1, negative 5). Triangle R S T has points (1, 1), (1, 5), and (4, 1).

Question illustration
A
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the x-axis and a translation 2 units to the left.
B
The figures are congruent. ΔRST can be mapped to ΔACB by a reflection over the y-axis and a translation 2 units down.
C
The figures are not congruent. Point R corresponds to point A, but S corresponds to B and T corresponds to C.
D
The figures are not congruent. Point R does not correspond with point A.
23

Triangles A B C and E D C are shown. Triangle A B C is rotated about point C to form triangle E D C.

Question illustration
A
a rotation about point B
B
a reflection across the line containing CB
C
a reflection across the line containing AC
D
a rotation about point C
24

Which congruence theorems can be used to prove ΔABR ≅ ΔACR? Select three options.HLSASSSSASAAAS

Question illustration
A
HL
B
SAS
C
SSS
D
ASA
E
AAS
25

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
26

Consider the diagram.

Question illustration
A
SSS.
B
ASA.
C
SAS.
D
HL.
27

Which pair of triangles can be proven congruent by the HL theorem?

A
2 right triangles have congruent hypotenuses.
Option A
B
2 triangles have one congruent angle and 2 congruent sides.
Option B
C
2 right triangles have congruent hypotenuses and another congruent side.
Option C
D
2 triangles have 3 congruent sides.
Option D
28

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
29

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
30

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.
31

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

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