Pythagorean Theorem Basics

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

To which shape(s) does the Pythagorean theorem apply?

Back

Right triangles only.

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 one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

How much is 4²?

Back

16.

Front

What is a leg in a right triangle?

Back

A leg is one of the two shorter sides of a right triangle that form the right angle.

Front

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

Back

8 (Using the Pythagorean theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).

Front

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

Back

The sum of the squares of the lengths of the two legs equals the square of the length of the hypotenuse.

Front

Can the Pythagorean theorem be used for non-right triangles?

Back

No, the Pythagorean theorem only applies to right triangles.

Front

If a right triangle has legs measuring 5 and 12, what is the hypotenuse?

Back

13 (Using the Pythagorean theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).