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# Triangle Inequality Theorem (Grade 9)

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## Triangle Inequality Theorem

Instructions: Use your knowledge of the triangle inequality theorem to answer the following questions.

1.
Is it possible for a triangle to have sides with the lengths 2 inches, 3 inches, and 6 inches?
1. Yes
2. No
2.
The sum of the lengths of two sides of a triangle is greater than the length of the third side.
1. True
2. False
3.
Which choice shows three lengths that cannot be the lengths of the three sides of a triangle?
1. 2, 3, 4
2. 5, 6, 9
3. 7, 2, 7
4. 7, 6, 14
4.
Which choice shows three lengths that can be the lengths of the three sides of a triangle?
1. 2, 6, 3
2. 5, 6, 11
3. 7, 2, 8
4. 7, 6, 14
5.
Which choice shows three lengths that cannot be the lengths of the three sides of a triangle?
1. 7, 3, 3
2. 5, 6, 9
3. 7, 2, 7
4. 7, 6, 11
6.
Which choice shows three lengths that cannot be the lengths of the three sides of a triangle?
1. 2, 3, 4
2. 5, 6, 12
3. 7, 2, 5
4. 7, 6, 12
7.
Which choice shows three lengths that cannot be the lengths of the three sides of a triangle?
1. 2, 3, 4
2. 5, 6, 9
3. 7, 7, 14
4. 7, 6, 12
8.
Which choice shows three lengths that can be the lengths of the three sides of a triangle?
1. 2, 3, 3
2. 5, 6, 11
3. 7, 2, 9
4. 7, 6, 14
9.
A triangle has one side that is 8 cm and another that is 16 cm. What is the range of possible measurements for the third side X?
1. $24 \ "cm" < X \ "cm" < 8 \ "cm"$
2. $24 \ "cm" < X \ "cm" <18 \ "cm"$
3. $18 \ "cm" < X \ "cm" <24 \ "cm"$
4. $8 \ "cm" < X \ "cm" <24 \ "cm"$
10.
What is the triangle inequality theorem?

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