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 one side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

Given two sides of a triangle measuring 7 ft and 13 ft, what is the range for the length of the third side?

Back

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

Front

How do you determine the longest side of a triangle?

Back

The longest side of a triangle is opposite the largest angle.

Front

If the angles of a triangle are ∠A, ∠B, and ∠C, how are they related to the side lengths?

Back

The side lengths are proportional to the angles opposite them; the larger the angle, the longer the side.

Front

What is the relationship between the smallest angle and the smallest side in a triangle?

Back

The smallest angle is opposite the smallest side.

Front

If a triangle has sides of lengths 5, 7, and 12, does it satisfy the Triangle Inequality Theorem?

Back

No, because 5 + 7 is not greater than 12.

Front

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

Back

The triangle is degenerate, meaning it collapses into a straight line.

Front

List the angles in order from smallest to largest if ∠A = 30°, ∠B = 60°, ∠C = 90°.

Back

∠A, ∠B, ∠C.

Front

What is the minimum length of the third side if two sides of a triangle measure 8 and 10?

Back

The minimum length of the third side must be greater than 2 (8 - 10).