Pythagorean Theorem 8.6C, 8.7C D

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 are the side lengths of a right triangle?

Back

In a right triangle, the side lengths must satisfy the Pythagorean Theorem. For example, if a = 3 and b = 4, then c = 5, because 3² + 4² = 5².

Front

How do you find the length of the hypotenuse?

Back

To find the length of the hypotenuse in a right triangle, use the formula c = √(a² + b²).

Front

What is a right triangle?

Back

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

Front

Which set of side lengths forms a right triangle? 6, 9, 12 or 8, 10, 12 or 9, 40, 41 or 5, 10, 12?

Back

The set of side lengths 9, 40, 41 forms a right triangle.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root.

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10, because 6² + 8² = 10².

Front

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

Back

It means that one of its angles is exactly 90 degrees.

Front

Which set of side lengths does not form a right triangle? 38, 80, 90 or 16, 63, 65 or 14, 15, 29?

Back

The set of side lengths 14, 15, 29 does not form a right triangle.

Front

How do you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths.