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

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle and is always the longest side of the triangle.

Front

If a right triangle has sides of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

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

Back

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

Front

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

Back

The relationship is defined by the Pythagorean Theorem: c² = a² + b².

Front

If one side of a right triangle is 5 and the hypotenuse is 13, what is the length of the other side?

Back

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

Front

What is the formula to find the length of the hypotenuse?

Back

The formula is c = √(a² + b²).

Front

In a right triangle, if the lengths of the legs are 8 and 15, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 8² + 15²; c² = 64 + 225; c² = 289; c = 17.

Front

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

Back

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

Front

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

Back

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