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 is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What does it mean for a triangle to be a right triangle?

Back

A triangle is a right triangle if it satisfies the Pythagorean Theorem, meaning the square of the longest side equals the sum of the squares of the other two sides.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

Yes, because 3² + 4² = 5² (9 + 16 = 25).

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

What is the converse of the Pythagorean Theorem?

Back

The converse of the Pythagorean Theorem states that if a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

To determine if a triangle is a right triangle, check if the square of the longest side equals the sum of the squares of the other two sides.

Front

If the sides of a triangle are 2.1, 7.2, and 7.5, is it a right triangle?

Back

Yes, because 2.1² + 7.2² = 7.5² (4.41 + 51.84 = 56.25).

Front

What are the side lengths of a right triangle?

Back

The side lengths of a right triangle can be any three positive numbers that satisfy the Pythagorean Theorem.

Front

Can the lengths 9, 12, and 15 form a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).