Triangle Inequality Theorem Problems

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 side lengths 3, 5, and 5 form a triangle?

Back

Yes, because 3 + 5 > 5, 5 + 5 > 3, and 3 + 5 > 5.

Front

What is the condition for three lengths to form a triangle?

Back

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

Front

If side lengths are 15 in., 12 in., and 2 in., can they form a triangle?

Back

No, because 15 + 2 is not greater than 12.

Front

What is the longest side in a triangle with sides 5, 7, and 9?

Back

9 is the longest side.

Front

In triangle JKL, if side lengths are 4, 5, and 10, what mistake did Scott make?

Back

These side lengths could not form a triangle because 4 + 5 is not greater than 10.

Front

What is the largest angle in a triangle?

Back

The largest angle is opposite the longest side.

Front

If side lengths are 6, 8, and 10, can they form a triangle?

Back

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

Front

What is the relationship between the longest side and the angles in a triangle?

Back

The longest side is always opposite the largest angle.

Front

Can the side lengths 7, 3, and 4 form a triangle?

Back

Yes, because 7 + 3 > 4, 7 + 4 > 3, and 3 + 4 > 7.