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 is the formula to find the length of the hypotenuse in a right triangle?

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²), where a and b are the lengths of the other two sides.

Front

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

Back

The length of the hypotenuse is 5 cm, calculated as c = √(3² + 4²) = √(9 + 16) = √25 = 5.

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 the Pythagorean Theorem, if a = 5 and c = 13, what is the length of b?

Back

The length of b is 12, calculated as b = √(c² - a²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

Front

True or False: The Pythagorean Theorem can be used for any triangle.

Back

False. The Pythagorean Theorem only applies to right triangles.

Front

What is the relationship between the sides of a right triangle according to the Pythagorean Theorem?

Back

The relationship is that the sum of the squares of the two shorter sides (legs) equals the square of the longest side (hypotenuse): a² + b² = c².

Front

If a right triangle has legs of lengths 6 cm and 8 cm, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10 cm, calculated as c = √(6² + 8²) = √(36 + 64) = √100 = 10.

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 hypotenuse of a right triangle is 15 cm and one leg is 9 cm, what is the length of the other leg?

Back

The length of the other leg is 12 cm, calculated as b = √(c² - a²) = √(15² - 9²) = √(225 - 81) = √144 = 12.