Pythagorean Theorem

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 hypotenuse in a right triangle?

Back

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

Front

If a triangle has sides of lengths 8, 15, and 17, which side is the hypotenuse?

Back

The hypotenuse is 17.

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

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 (a² + b² = c²).

Front

Find the length of the missing side if one side is 5 and the hypotenuse is 13.

Back

The missing side is 12, calculated using the Pythagorean Theorem: 5² + b² = 13².

Front

What are the side lengths of a 3-4-5 triangle?

Back

The side lengths are 3, 4, and 5, which satisfy the Pythagorean Theorem: 3² + 4² = 5².

Front

If a right triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

Yes, it is a right triangle because 6² + 8² = 10².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

If one side of a right triangle is 9 and the hypotenuse is 15, what is the length of the other side?

Back

The length of the other side is 12, calculated using the Pythagorean Theorem: 9² + b² = 15².

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.