Triangle Inequality Theorem

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If the lengths of two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (5 - 7) and less than 12 (5 + 7). So, the range is greater than 2 and less than 12.

Front

Identify the smallest angle in a triangle with sides 3, 4, and 5.

Back

The smallest angle is opposite the shortest side, which is 3.

Front

List the side measures in order from shortest to longest for a triangle with sides 6, 8, and 10.

Back

The side measures in order are 6, 8, 10.

Front

Which of these lengths CANNOT represent the sides of a triangle? 5, 10, 15, 30, 20

Back

30 cannot represent the sides of a triangle because 5 + 10 is not greater than 30.

Front

Given two sides of lengths 8 and 15, what is the range for the third side?

Back

The third side must be greater than 7 (15 - 8) and less than 23 (8 + 15). So, the range is greater than 7 and less than 23.

Front

What is the range of values for x if the sides of a triangle are 3 and 9?

Back

x must be between 7 and 12 (9 - 3 < x < 9 + 3).

Front

If one side of a triangle is 12 and another is 5, what lengths can the third side be?

Back

The third side can be between 7 and 17 (12 - 5 < x < 12 + 5).

Front

What is the relationship between the angles and sides of a triangle?

Back

In a triangle, the larger the angle, the longer the opposite side.

Front

If a triangle has sides of lengths 7, 10, and 12, does it satisfy the Triangle Inequality Theorem?

Back

Yes, 7 + 10 > 12, 7 + 12 > 10, and 10 + 12 > 7.