Pythagorean Theorem & Converse

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Formula: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

If a triangle has sides of lengths 4, 5, and 6, is it a right triangle?

Back

No, it is not a right triangle.

Front

Identify the hypotenuse in a right triangle with sides 6, 7, and 3.

Back

The hypotenuse is 7.

Front

What is the formula for the Pythagorean Theorem?

Back

The formula is a² + b² = c².

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can the Pythagorean Theorem be used for obtuse triangles?

Back

No, the Pythagorean Theorem cannot be used for obtuse triangles.

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has side lengths a, b, and c, and a² + b² = c², 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, it is a right triangle because 5² + 12² = 13².

Front

What is the hypotenuse of a right triangle with legs of lengths 8 and 15?

Back

The hypotenuse is 17, since 8² + 15² = 17².