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). It can be expressed as: a² + b² = c².

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

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

Back

5 feet (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

What is the length of the hypotenuse if the legs of a right triangle are 6 feet and 8 feet?

Back

10 feet (6² + 8² = 36 + 64 = 100; √100 = 10).

Front

In a right triangle, if one leg is 5 feet and the hypotenuse is 13 feet, what is the length of the other leg?

Back

12 feet (using the Pythagorean Theorem: 5² + b² = 13²; 25 + b² = 169; b² = 144; b = 12).

Front

What is a right angle?

Back

A right angle is an angle that measures exactly 90 degrees.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and it is the longest side.

Front

If a ladder is placed against a wall forming a right triangle, how can you find the height of the wall?

Back

You can use the Pythagorean Theorem: height² + distance from the wall² = ladder length².

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

What type of angle do the legs of a right triangle form?

Back

The legs of a right triangle form a right angle.