AnswersMCHS CR25 - GEOMETRYUnit Test

Unit Test — Unit test Answers

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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
2
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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
3

Quadrilateral ABCD is translated down and left to form quadrilateral OLMN.

Question illustration
A
5 units
B
6 units
C
8 units
D
10 units
4

Triangle KNM is shown.

Question illustration
A
KN = NM
B
KN + NM = KM
C
KM = 2(NM)
D
KN = KM
Option D
5

In which figure is point G a centroid?

A
Triangle A B C is a right triangle. Lines are drawn from each point to the opposite side and intersect at point G.
Option A
B
Triangle F D E is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each line segment splits each side into 2 equal parts.
Option B
C
Triangle L M N is shown. Lines are drawn from each point to the opposite side and intersect at point G. Each angle has a different measure.
Option C
D
Triangle H J K is shown. Lines are drawn from each point to the opposite side to form right angles and they intersect at point G.
Option D
6

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
7

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
8

Triangle A B C is shown. Lines are drawn from each point to the opposite side and intersect at point D. They form line segments A G, B E, and C F.

Question illustration
A
BE, CF, and AG are angle bisectors.
B
BE ⊥ AC, AG ⊥ BC, and CF ⊥ AB.
C
BE bisects AC, CF bisects AB, and AG bisects BC.
D
BE is a perpendicular bisector of AC, CF is a perpendicular bisector of AB, and AG is a perpendicular bisector of BC.
9

Which must be true? Select two options.

A
Point H is the center of the circle that passes through points D, E, and F.
B
Point H is the center of the circle that passes through points L, M, and N.
C
Line segment H E is-congruent-to line segment H D
Option C
D
Line segment L H is-congruent-to line segment N H
Option D
E
Line segment F L is-congruent-to line segment F N
Option E
10

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°.
11

Chang knows one side of a triangle is 13 cm. Which set of two sides is possible for the lengths of the other two sides of this triangle?

A
5 cm and 8 cm
B
6 cm and 7 cm
C
7 cm and 2 cm
D
8 cm and 9 cm
12

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
13

Three quadrilaterals exist such that GHJK ≅ ASDF and GHJK ≅ VBNM.If MV measures 3 cm, which other segment must measure 3 cm?

A
AF
B
KJ
C
FD
D
GJ
14

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.
15

Point Z is the incenter of ΔSRT.

Question illustration
A
24°
B
31°
C
35°
D
62°
16

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.
17

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.
18

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
19

Triangles J K L and M N R are shown.

Question illustration
A
KL ≅ NR
B
∠L ≅ ∠R
C
∠K ≅ ∠N
D
JK ≅ MN
20

Quadrilateral L M N O is reflected over a line to form quadrilateral C D A B.

Question illustration
A
AB
B
AD
C
CB
D
DC

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