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 is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

In a right triangle, which side is always opposite the right angle?

Back

The hypotenuse is always 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

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

Front

True or False: The hypotenuse can be shorter than either leg in a right triangle.

Back

False. The hypotenuse is always the longest side.

Front

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

Back

Using the Pythagorean Theorem: c² = a² + b²; 13² = 5² + b²; 169 = 25 + b²; b² = 144; b = 12.

Front

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

Back

The formula is 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

Using the Pythagorean Theorem: c² = 9² + 12²; c² = 81 + 144; c² = 225; c = 15.

Front

What do you call the two shorter sides of a right triangle?

Back

The two shorter sides of a right triangle are called the legs.

Front

If the lengths of the legs of a right triangle are equal, what type of triangle is it?

Back

It is an isosceles right triangle.