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: c² = a² + b².

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. They are usually referred to as sides a and b.

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 6 and the other leg is 8, what is the length of the hypotenuse?

Back

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

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

Front

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Back

12 (Using the Pythagorean Theorem: 13² = 5² + b² => 169 = 25 + b² => b² = 144 => b = √144 = 12).

Front

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

Back

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

Front

If a right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Back

15 (Using the Pythagorean Theorem: c² = 9² + 12² => c² = 81 + 144 => c² = 225 => c = √225 = 15).

Front

True or False: The Pythagorean Theorem can only be used for right triangles.

Back

True.

Front

What do you call the side opposite the right angle in a right triangle?

Back

The hypotenuse.