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

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

Identify the smallest angle in a triangle with angles ∠K, ∠L, and ∠M if ∠L is the smallest.

Back

∠L is the smallest angle.

Front

What is the measure of the missing angle if the other two angles are 47° and 86°?

Back

The missing angle is 47°.

Front

Will the line segments with lengths 2, 3, and 6 form a triangle?

Back

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

Front

If Sally has two sides of a triangle measuring 7 in and 11 in, what is a possible length for the third side?

Back

The third side could be 8 in.

Front

What is the minimum length of a side in a triangle if the other two sides are 5 and 7?

Back

The minimum length must be greater than 2 (5 - 7 < x < 5 + 7).

Front

What is the maximum length of a side in a triangle if the other two sides are 4 and 9?

Back

The maximum length can be less than 13 (4 + 9 > x).

Front

If a triangle has sides of lengths 10, 6, and x, what is the range of possible values for x?

Back

x must be greater than 4 and less than 16 (10 - 6 < x < 10 + 6).

Front

What happens if the sum of two sides of a triangle equals the length of the third side?

Back

The segments will be collinear and will not form a triangle.