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Triangle Inequalities Answers

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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.
2
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Choose the word that correctly completes the statement.

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A
adjacent
B
included
C
longest
D
shortest
3

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
4

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
5

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
6

Lee is creating a garden with the dimensions shown.

Question illustration
A
The path along is longer than the path along , and the path along is longer than the path along .
Option A
B
The path along is longer than the path along , and the path along is longer than the path along .
Option B
C
The path along is longer than the path along , and the path along is longer than the path along .
Option C
D
The path along is longer than the path along , and the path along is longer than the path along .
Option D
7

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.
8

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
9

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
10

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.

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