Triangle Inequality Theorem (Ordering and Forming Triangles)

Front

What is the Triangle Inequality Theorem?

Back

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

Front

Which sets of side lengths can form a triangle?

Back

A set of side lengths can form a triangle if they satisfy the Triangle Inequality Theorem.

Front

Given side lengths 3, 6, and 12, do they form a triangle?

Back

No, because 3 + 6 is not greater than 12.

Front

Given side lengths 7, 7, and 14, do they form a triangle?

Back

No, because 7 + 7 is not greater than 14.

Front

Given side lengths 9, 9, and 9, do they form a triangle?

Back

Yes, because 9 + 9 is greater than 9.

Front

Given side lengths 13, 6, and 7, do they form a triangle?

Back

Yes, because 13 < 6 + 7.

Front

If two sides of a triangle are 7 ft and 13 ft, what is the range for the third side?

Back

The third side must be more than 6 ft but less than 20 ft.

Front

How do you order side lengths from shortest to longest?

Back

List the side lengths in ascending order.

Front

What is the longest side in a triangle with sides AC, BA, and BC?

Back

AC is the longest side.

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.