Pythagorean Theorem Practice

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 is expressed as a² + b² = c².

Front

What does a² + b² = c² represent?

Back

It represents the relationship between the lengths of the sides of a right triangle, where 'a' and 'b' are the lengths of the legs and 'c' is the length of the hypotenuse.

Front

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

Back

5 cm (using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25, so c = √25 = 5).

Front

Does the set of numbers 8, 15, 17 represent a right triangle?

Back

Yes, because 8² + 15² = 17² (64 + 225 = 289).

Front

What is the hypotenuse of a right triangle with legs measuring 6 cm and 8 cm?

Back

10 cm (using the Pythagorean Theorem: 6² + 8² = 36 + 64 = 100, so c = √100 = 10).

Front

If the hypotenuse of a right triangle is 10 cm and one leg is 6 cm, how long is the other leg?

Back

8 cm (using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64, so the other leg is √64 = 8).

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 shorter sides (legs) equals the square of the longest side (hypotenuse).

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If a ladder is placed 12 feet away from a wall and reaches a height of 16 feet, how long is the ladder?

Back

20 feet (using the Pythagorean Theorem: 12² + 16² = 144 + 256 = 400, so c = √400 = 20).

Front

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

Back

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