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). It can be expressed as: a² + b² = c².

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

Front

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

Back

Yes, because 7² + 24² = 49 + 576 = 625, which is equal to 25².

Front

What are the side lengths of a right triangle?

Back

In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides are called the legs.

Front

Which side is the hypotenuse in a right triangle with sides a, b, and c?

Back

The hypotenuse is the longest side, typically denoted as c.

Front

What is an example of a set of side lengths that does not form a right triangle?

Back

The side lengths 14, 15, and 29 do not form a right triangle because 14² + 15² ≠ 29².

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).

Front

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

Back

The hypotenuse is 41, as it is the longest side.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

To find a missing side, use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse.