Unit Test — Unit test Answers

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

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A
AB = 25
B
27 < AB < 81
C
AB = 85
D
AB 81
2
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A regular pentagon is created using the bases of five congruent isosceles triangles, joined at a common vertex.

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A
54°
B
72°
C
108°
D
144°
3

In the triangles, and .

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A
congruent to
B
longer than
C
shorter than
D
the same length as
4

Consider triangle WXY.

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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.
5

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
6

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
7

Triangle KNM is shown.

Question illustration
A
KN = NM
B
KN + NM = KM
C
KM = 2(NM)
D
KN = KM
Option D
8

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°
9

Nigel and Mia are searching for a treasure chest under water. The straight line distance between them is 100 meters.

Question illustration
A
Nigel is closer because his distance to the chest is opposite the larger angle.
B
Mia is closer because her distance to the chest is opposite the smaller angle.
C
Nigel is closer because his distance from the chest is 100 meters.
D
Mia is closer because her distance from the chest is 100 meters.
10

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°
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

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
13

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°.
14

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°.
15

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
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

Based on the given angle measures, which triangle has side length measures that could be correct?

A
A right triangle is shown. The length of the hypotenuse is 16, the base is 8, and the other side is 13.9. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Option A
B
A right triangle is shown. The length of the hypotenuse is 13.9, the base is 8, and the other side is 16. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Option B
C
A right triangle is shown. The length of the hypotenuse is 13.9, the base is 16, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Option C
D
A right triangle is shown. The length of the hypotenuse is 16, the base is 13.9, and the other side is 8. The top angle is 60 degrees and the bottom right angle is 30 degrees.
Option D
18

In the triangles, QR = DE and SR = FE.

Question illustration
A
QS = DF
B
DF < QS
C
QS < DE
D
SR = DE
19

is a perpendicular bisector of .

Question illustration
A
It will be a right triangle.
B
It will be an acute triangle.
C
It will be an equilateral triangle.
D
It will be an isosceles triangle.
20

The side lengths of triangle ABC are written in terms of the variable p, where p ≥ 3.

Question illustration
A
mA > mC > mB
Option A
B
mB > mA > mC
Option B
C
mC > mA > mB
Option C
D
mC > mB > mA
Option D

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