Triangle Inequality Theorem

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

Can the lengths 9, 3, and 10 form a triangle?

Back

Yes, because 9 + 3 > 10, 9 + 10 > 3, and 3 + 10 > 9.

Front

Can the lengths 11, 7, and 21 form a triangle?

Back

No, because 11 + 7 is not greater than 21.

Front

Can the lengths 6, 5, and 8 form a triangle?

Back

Yes, because 6 + 5 > 8, 6 + 8 > 5, and 5 + 8 > 6.

Front

Can the lengths 18, 7, and 10 form a triangle?

Back

No, because 18 + 7 is not greater than 10.

Front

Can the lengths 6, 10, and 8 form a triangle?

Back

Yes, because 6 + 10 > 8, 6 + 8 > 10, and 10 + 8 > 6.

Front

What is the first condition of the Triangle Inequality Theorem?

Back

The sum of the lengths of the two shorter sides must be greater than the length of the longest side.

Front

What is the second condition of the Triangle Inequality Theorem?

Back

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

Front

If a triangle has sides of lengths 5, 12, and 13, can it exist?

Back

Yes, because 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5.

Front

If a triangle has sides of lengths 2, 3, and 6, can it exist?

Back

No, because 2 + 3 is not greater than 6.