4.2: Pythagorean Theorem & Converse

Front

What is the formula for the Pythagorean theorem?

Back

a² + b² = c², where c is the hypotenuse.

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the longest side, opposite the right angle.

Front

How can you determine if three lengths can form a right triangle?

Back

Use the Pythagorean theorem: check if a² + b² = c² for the lengths.

Front

What are the side lengths of a right triangle if the lengths are 33, 56, and 65?

Back

These lengths form a right triangle because 33² + 56² = 65².

Front

What is the converse of the Pythagorean theorem?

Back

If a² + b² = c², then the triangle is a right triangle.

Front

Can a triangle with sides 8 in, 10 in, and 12 in be a right triangle?

Back

No, because 8² + 10² ≠ 12².

Front

What is the relationship between the sides of a right triangle?

Back

The sum of the squares of the two shorter sides equals the square of the longest side.

Front

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

Back

Yes, because 5² + 12² = 13².

Front

What is the definition of a right triangle?

Back

A triangle that has one angle measuring 90 degrees.

Front

What is the significance of the hypotenuse in a right triangle?

Back

It is the longest side and is used in the Pythagorean theorem.