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 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, it can be any length between 2 and 12.

Front

Can a triangle have sides of lengths 3, 4, and 8?

Back

No, because 3 + 4 is not greater than 8.

Front

What is the minimum length of the third side if two sides are 10 and 15?

Back

The minimum length of the third side must be greater than 5 (15 - 10).

Front

What is the maximum length of the third side if two sides are 10 and 15?

Back

The maximum length of the third side must be less than 25 (10 + 15).

Front

Which of the following sets can represent the sides of a triangle: {3, 4, 5}, {1, 2, 3}, {5, 10, 15}?

Back

{3, 4, 5} can represent the sides of a triangle; {1, 2, 3} and {5, 10, 15} cannot.

Front

If a triangle has sides of lengths 6 and 8, what is a possible length for the third side?

Back

A possible length for the third side is 9 (6 + 8 > 9).

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

In triangle ABC, if AB = 10 and BC = 17, what could be the length of AC?

Back

AC could be 16 inches, as it satisfies the Triangle Inequality Theorem.

Front

Which of the following would NOT work to make a triangle with sides 2 and 6?

Back

4 would not work because 2 + 6 > 4, but 2 + 4 is not greater than 6.