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 hypotenuse in a right triangle?

Back

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

Front

If a right triangle has sides of lengths 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

In a right triangle, if one leg is 8 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b²; 10² = 8² + b²; 100 = 64 + b²; b² = 36; b = 6.

Front

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

Back

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

Front

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

Back

In a right triangle, the sum of the squares of the two legs equals the square of the hypotenuse.

Front

If a right triangle has side lengths 9, 12, and 15, is it a right triangle?

Back

Yes, because 9² + 12² = 15² (81 + 144 = 225).

Front

What is the formula to find the length of a missing side in a right triangle?

Back

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

Front

If the lengths of the legs of a right triangle are 7 and 24, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 7² + 24²; c² = 49 + 576; c² = 625; c = 25.

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.