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 11, 1, and 12 form a triangle?

Back

No, because 11 + 1 is not greater than 12.

Front

What is the range of possible lengths for the third side of a triangle if two sides measure 10 and 7?

Back

Front

Can the lengths 8, 10, and 20 form a triangle?

Back

No, because 8 + 10 is not greater than 20.

Front

In triangle ABC, if AB = 10 inches and BC = 17 inches, what could be the length of side AC?

Back

AC could be 16 inches.

Front

Can the lengths 10, 18, and 12 form a triangle?

Back

Yes, because 10 + 12 > 18, 10 + 18 > 12, and 12 + 18 > 10.

Front

What is the first 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 one side of a triangle is 5 and another is 10, what is the maximum length of the third side?

Back

The maximum length of the third side is 14 (5 + 10 - 1).

Front

If two sides of a triangle are 6 and 8, what is the minimum length of the third side?

Back

The minimum length of the third side is 3 (8 - 6 + 1).

Front

What is an example of a set of lengths that cannot form a triangle?

Back

Lengths 2, 3, and 6 cannot form a triangle because 2 + 3 is not greater than 6.