Converse of the Pythagorean Theorem

Front

What is the Converse of the Pythagorean Theorem?

Back

If in a triangle, the square of the length of one side 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

Yes, because 5² + 12² = 13² (25 + 144 = 169).

Front

What is the formula for the Pythagorean Theorem?

Back

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

Front

What are the legs of a right triangle?

Back

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

Front

What is the hypotenuse of a right triangle?

Back

The longest side of a right triangle, opposite the right angle.

Front

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 25² (49 + 576 = 625).

Front

Which set of side lengths does not form a right triangle: 8, 15, 17 or 7, 24, 25?

Back

7, 24, 25 forms a right triangle; 8, 15, 17 does not.

Front

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

Back

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If a triangle has sides of lengths 9, 40, and 41, which side is the hypotenuse?

Back

41.

Front

What is the significance of the Pythagorean Theorem in geometry?

Back

It allows us to determine if a triangle is a right triangle based on the lengths of its sides.