AnswersMHS - Geometry - S1 - CRUnit 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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Triangle XYZ is isosceles. Angle Y measures a°.

Question illustration
A
2a
B
StartFraction a Over 2 EndFraction
Option B
C
90 a
Option C
D
180 2a
Option D
3

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.
4

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.
5

Triangle JKL is isosceles. The measure of angle J is 72° and the measure of angle K is 36°. Which statement describes angle L?

A
Angle L is a base angle and measures 36°.
B
Angle L is a base angle and measures 72°.
C
Angle L is a vertex angle and measures 36°.
D
Angle L is a vertex angle and measures 72°.
6

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
7

2 horizontal and parallel lines are intersected by 2 diagonal lines to form a triangle with exterior angles. The top angle of the triangle is (2 x + 10) degrees. The bottom right angle of the triangle is 79 degrees. The exterior angle to the bottom left angle is (6 x + 1) degrees.

Question illustration
A
x = 2.25
B
x = 11.25
C
x = 13
D
x = 22
8

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
9

If isosceles triangle ABC has a 130° angle at vertex B, which statement must be true?

A
m∠A = 15° and m∠C = 35°
B
m∠A + m∠B = 155°
C
m∠A + m∠C = 60°
D
m∠A = 20° and m∠C = 30°
10

If triangle RST is an acute triangle, then m∠S must be

A
less than 90°.
B
equal to 90°.
C
equal to 100°.
D
greater than 90° and less than 180°.
11

The lengths of the sides of triangle XYZ are written in terms of the variable m, where m ≥ 6.

Question illustration
A
mX < mZ < mY
Option A
B
mY < mZ < mX
Option B
C
mY < mX < mZ
Option C
D
mZ < mY < mX
Option D
12

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
13

Triangle A B C is shown with its exterior angles. Line C B extends through point D. Line B C extends to form exterior angle that is 135 degrees. Angle C A B is 75 degrees.

Question illustration
A
m∠ABC = 15°
B
m∠ABC = 45°
C
m∠ABC = 60°
D
m∠ABC = 75°
14

Consider triangle WXY.

Question illustration
A
Angle W is greater than angle Y.
B
Angle Y is the largest angle.
C
Angle X is smaller than angle W.
D
Angle W is the smallest angle.
15

Which statements regarding the diagram of ΔEBC are true? Select three options.

A
∠BEC is an exterior angle.
B
∠DEC is an exterior angle.
C
∠ABE and ∠EBC are supplementary angles.
D
∠BCF and ∠DEC are supplementary angles.
E
∠BEC is a remote interior angle to exterior ∠BCF.
16

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
17

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
18

Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.

Question illustration
A
AB = 25
B
27 < AB < 81
C
AB = 85
D
AB 81
19

Triangle K M L is shown. Line L K extends through point J to form exterior angle J K M.

Question illustration
A
∠JKL
B
∠MKL
C
∠KLM
D
∠LMK
20

In the triangles, and .

Question illustration
A
congruent to
B
longer than
C
shorter than
D
the same length as

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