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Triangle Inequalities Answers

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In the triangles, and .

Question illustration
A
and are the same length.
Option A
B
is longer than .
Option B
C
is shorter than .
Option C
D
is shorter than or the same length as .
Option D
2
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In the triangles, XY = MP and YZ = PN.

Question illustration
A
mY = 80°
Option A
B
mY = 85°
Option B
C
mY = 100°
Option C
D
mY = 180°
Option D
3

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
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

Choose the word that correctly completes the statement.

Question illustration
A
adjacent
B
included
C
longest
D
shortest
6

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
7

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.
8

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.
9

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.
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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