Triangle Inequality and Pythagorean Converse

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

If two sides of a triangle are 8 and 12, what is the range of possible lengths for the third side?

Back

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

Do the side lengths 2, 2, and 4 form a triangle?

Back

No, they do not form a triangle because 2 + 2 is not greater than 4.

Front

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

Back

The length of side AC could be 16 inches.

Front

Is it possible for a triangle to have side lengths of 1, 1, and 3?

Back

No, these lengths do not satisfy the Triangle Inequality Theorem.

Front

What is the Pythagorean Theorem?

Back

Front

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if the square of the length of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Front

What is the minimum length of the third side of a triangle if the other two sides are 8 and 12?

Back