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 in a right triangle?

Back

The formula for finding the hypotenuse is a² + b² = c².

Front

In a right triangle, if one side is 3 units and the other side is 4 units, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 5 units (3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

The length of the hypotenuse is 13 units (5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is a right triangle?

Back

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

Front

If the hypotenuse of a right triangle is 10 units and one leg is 6 units, what is the length of the other leg?

Back

The length of the other leg is 8 units (10² - 6² = 100 - 36 = 64; √64 = 8).

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The relationship is that the sum of the squares of the two legs equals the square of the hypotenuse.

Front

Can the Pythagorean Theorem be used for obtuse or acute triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

If a right triangle has legs of lengths 8 units and 15 units, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 17 units (8² + 15² = 64 + 225 = 289; √289 = 17).