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). Formula: a² + b² = c².

Front

What is the formula for finding the hypotenuse?

Back

The formula for finding the hypotenuse in a right triangle is a² + b² = c².

Front

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

Back

10 (Using the Pythagorean Theorem: 6² + 8² = c², 36 + 64 = c², 100 = c², c = 10).

Front

What is a right triangle?

Back

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

Front

If the lengths of the two legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

13 (Using the Pythagorean Theorem: 5² + 12² = c², 25 + 144 = c², 169 = c², c = 13).

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle.

Front

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

Back

12 (Using the Pythagorean Theorem: 9² + b² = 15², 81 + b² = 225, b² = 144, b = 12).

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.

Front

What is the length of x if one leg is 7 and the hypotenuse is 25?

Back

24 (Using the Pythagorean Theorem: 7² + x² = 25², 49 + x² = 625, x² = 576, x = 24).

Front

What is the area of a right triangle with legs of length 3 and 4?

Back

6 (Area = 1/2 * base * height = 1/2 * 3 * 4 = 6).