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

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 (hypotenuse) is equal to the sum of the squares of the other two sides.

Front

Given the sides 6 in, 8 in, and 10 in, is this a right triangle?

Back

Yes, because 6² + 8² = 36 + 64 = 100 = 10².

Front

What is the hypotenuse in a right triangle?

Back

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

Front

If the sides of a triangle are 9, 40, and 41, which is the hypotenuse?

Back

41 is the hypotenuse.

Front

What does it mean if a triangle is not a right triangle?

Back

If a triangle is not a right triangle, it means that none of its angles measure 90 degrees.

Front

If a = 2.1, b = 7.2, and c = 7.5, is this a right triangle?

Back

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

Front

What is the converse of the Pythagorean Theorem?

Back

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

Front

Can a triangle with sides 5, 12, and 13 be a right triangle?

Back

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