AnswersPA-Geometry AUnit Test

Triangle Inequalities Answers

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1
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Consider the triangles shown.

Question illustration
A
VU < US < SR by the hinge theorem.
B
VU = US = SR by the hinge theorem.
C
mUTV = mUST = mSTR by the converse of the hinge theorem.
Option C
D
mUTV > mUTS > mSTR by the converse of the hinge theorem.
Option D
2
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Consider the triangle.

Question illustration
A
Each side has a different length.
B
Two sides have the same length, which is less than the length of the third side.
C
The three sides have the same length.
D
The sum of the lengths of two sides is equal to the length of the third side.
3

In the triangles, and .

Question illustration
A
Angle G is congruent to angle P.
B
Angle G is smaller than angle P.
C
Angle G is larger than angle P.
D
Angle G is congruent to angle N.
4

Triangle T U V is shown. Side T U has a length of 5 units, side U V has a length of 8 units, and side T V has a length of 11 units.

Question illustration
A
Angle T is the smallest angle.
B
Angle V is the smallest angle.
C
Angles U and V must be equal.
D
Angles U and T must be equal.
5

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

Question illustration
A
QS = DF
B
DF < QS
C
QS < DE
D
SR = DE
6

Which statements are true regarding the sides and angles of the triangle? Select three options.

A
is the longest side.
Option A
B
Angle X is the largest angle.
C
Angle Z is greater than angle Y.
D
is opposite the largest angle.
Option D
E
is the shortest side.
Option E
7

Consider the triangle.

Question illustration
A
angle A, angle B, angle C
B
angle B, angle A, angle C
C
angle B, angle C, angle A
D
angle C, angle A, angle B
8

Consider the two triangles.

Question illustration
A
By the converse of the hinge theorem, mC = mS.
Option A
B
By the hinge theorem,TS > AC.
C
By the converse of the hinge theorem, mS > mC.
Option C
D
By the hinge theorem, BA = RT.
9

In the diagram, MQ = QP = PO = ON.

Question illustration
A
Segment OP is longer than segment MQ.
B
Segment MN has the same length as segment MP.
C
The measure of angle Q equals the measure of angle O.
D
Angle O is larger than angle Q.
10

Gene starts from home and travels 3 miles north to the shopping mall. From the shopping mall, he travels 2 miles west to the library. Then, from the library, he travels about 3.6 miles to return home. The entire trip forms a triangle.

Question illustration
A
at his home
B
at the mall
C
between the mall and the library
D
between his home and the library

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Triangle Inequalities Answers — PA-Geometry A