AnswersALC EAP Geometry AUnit Test

Unit Test — Unit test Answers

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The proof that ΔQPT ≅ ΔQRT is shown.Given: SP ≅ SRProve: ΔQPT ≅ ΔQRT

Question illustration
A
definition of perpendicular bisector
B
definition of congruence
C
reflexive property
D
substitution property
2
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Triangles L O A and L A M share side L A. Angles O L A and A L M are congruent.

Question illustration
A
LO ≅ LM
B
OA ≅ MA
C
LOA ≅ LMA
Option C
D
LAO ≅ LAM
Option D
3

Two sides and the non-included right angle of one right triangle are congruent to the corresponding parts of another right triangle. Which congruence theorem can be used to prove that the triangles are congruent?

A
AAS
B
SSS
C
SAS
D
HL
4

Which congruence theorem can be used to prove △WXS ≅ △YZS?

Question illustration
A
SSS
B
ASA
C
SAS
D
HL
5

The triangles are congruent by the SSS congruence theorem.

Question illustration
A
reflection only
B
rotation only
C
translation, then reflection
D
translation, then rotation
6

Triangles A B C and Q R S are shown. Sides A B and Q R are congruent. Angles C A B and R Q S are congruent. Angles Q S R and A C B are congruent.

Question illustration
A
a reflection across the line containing AB
B
a rotation about point B
C
a reflection across the line containing CB
D
a rotation about point C
7

Which pair of triangles can be proven congruent by SAS?

A
2 identical triangles are shown. The triangle is reflected across a line to form the second triangle.
Option A
B
2 identical triangles are shown. The triangle is rotated 90 degrees to form the second triangle.
Option B
C
2 identical triangles are shown. The triangle is reflected across a line and then rotated to form the second triangle.
Option C
D
2 identical triangles are shown. The triangle is rotated up and to the left 90 degrees to form the second triangle.
Option D
8

Triangles J K L and M N R are shown.

Question illustration
A
KL ≅ NR
B
∠L ≅ ∠R
C
∠K ≅ ∠N
D
JK ≅ MN
9

Triangle L M Q is cut by perpendicular bisector L N. Angle N L Q is 32 degrees and angle L M N is 58 degrees.

Question illustration
A
Yes, they are congruent by either ASA or AAS.
B
Yes, they are both right triangles.
C
No, M is not congruent to NLQ.
Option C
D
No, there are no congruent sides.
10

Triangles Q R S and A B C are shown. The lengths of sides Q R and A B are 16 centimeters. The lengths of sides R S and B C are 24 centimeters. Angles Q R S and A B C are right angles. Sides Q S and A C are parallel and identical to each other and there is space in between the 2 triangles.

Question illustration
A
No, ΔQRS and ΔABC are congruent but ΔQRS cannot be mapped to ΔABC using a series rigid transformations.
B
No, ΔQRS and ΔABC are not congruent.
C
Yes, ΔQRS can be translated so that R is mapped to B and then rotated so that S is mapped to C.
D
Yes, ΔQRS can be translated so that Q is mapped to A and then reflected across the line containing QS.
11

The proof that MNG ≅ KJG is shown.Given: N and J are right angles; NG ≅ JGProve: MNG ≅ KJG

Question illustration
A
the reflexive property
B
ASA
C
AAS
D
the third angle theorem
12

Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.

Question illustration
A
Yes, if JL ≅ XZ.
B
Yes, if XZ = 10.
C
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
D
No, because the leg of one triangle is equal in length to the leg of the other triangle.
13

Triangles H J K and L M N are shown. The triangles have identical side lengths and angle measures. Triangle H J K is slightly lower and to the left of triangle L M N. Triangle H J K is reflected to form triangle L M N.

Question illustration
A
Translate K to N and reflect across the line containing HJ.
B
Translate K to N and reflect across the line containing JK.
C
Translate H to L and reflect across the line containing JK.
D
Translate K to L and reflect across the line containing HJ.
14

Given: bisects ∠MRQ; ∠RMS ≅ ∠RQS

Question illustration
A
ΔMNR ≅ ΔMNS by ASA
B
ΔRMS ≅ ΔRQS by AAS
C
ΔSNQ ≅ ΔSNM by SSS
D
ΔQNR ≅ ΔMNR by HL
15

Triangles D E F and G H J are congruent. Triangle D E F is shifted down and to the right to form triangle G H J.

Question illustration
A
dilation
B
reflection
C
rotation
D
translation
16

The proof that HG ≅ EG is shown.Given: G is the midpoint of KFKH ∥ EFProve: HG ≅ EGWhat is the missing reason in the proof?StatementReason1. ∠EGF ≅ ∠HGK1. vert. ∠s are ≅2. KH ∥ EF2. given3. ∠F ≅ ∠K3. alt. int. ∠s are ≅4. G is the midpoint of KF4. given5. FG ≅ KG5. def. of midpt.6. △FEG ≅ △KHG6. ?7. HG ≅ EG7. CPCTC

Question illustration
A
SAS
B
ASA
C
AAS
D
HL
17

The triangles shown are congruent by the SSS congruence theorem.

Question illustration
A
rotation, then reflection, then translation
B
rotation, then translation, then reflection
C
translation, then reflection, then rotation
D
translation, then rotation, then reflection
18

Triangles ABC and DEF have the following characteristics:∠B and ∠E are right angles∠A ≅ ∠DBC ≅ EF

A
AAS
B
ASA
C
HL
D
SAS
19

Triangles A Q R and A K P share point A. Triangle A Q R is rotated up and to the right for form triangle A Q R.

Question illustration
A
a rotation about point A
B
a reflection across the line containing AR
C
a reflection across the line containing AQ
D
a rotation about point R
20

Triangles L K N and P Q M are shown. Sides K L and Q P are congruent. Angles L K N and P Q M are right angles.

Question illustration
A
NL ≅ MP
B
NK ≅ MQ
C
N ≅ M
Option C
D
L ≅ P
Option D

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