Pythagorean Theorem Review

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: c² = a² + b².

Front

Identify the hypotenuse in a right triangle with sides 6, 6.7, and 3.

Back

The hypotenuse is the longest side of the triangle, which is 6.7.

Front

If one side of a right triangle is 9 and the other is 40, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 9² + 40² = 81 + 1600 = 1681. Therefore, c = √1681 = 41.

Front

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

Back

To find a missing side, rearrange the Pythagorean Theorem: a² = c² - b² or b² = c² - a², depending on which side is missing.

Front

Find the missing side if the hypotenuse is 80 and one side is 20.

Back

Using the Pythagorean Theorem: a² = 80² - 20² = 6400 - 400 = 6000. Therefore, a = √6000 ≈ 77.46.

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 a right triangle has sides of lengths 6.4 and 6.2, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 6.4² + 6.2² = 40.96 + 38.44 = 79.4. Therefore, c = √79.4 ≈ 8.9.

Front

What is the significance of the hypotenuse in a right triangle?

Back

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

Front

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

Back

A triangle is a right triangle if the square of the length of the longest side equals the sum of the squares of the other two sides (Pythagorean Theorem).

Front

Find the missing side if the hypotenuse is 72 and one side is 48.

Back

Using the Pythagorean Theorem: a² = 72² - 48² = 5184 - 2304 = 2880. Therefore, a = √2880 ≈ 53.67.