Pythagorean Theorem Practice

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle, typically labeled as 'a' and 'b'.

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

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

Back

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

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

Can the lengths 20, 25, and 15 form a right triangle?

Back

Yes, because 20² + 15² = 400 + 225 = 625 = 25².

Front

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

Back

To find a missing side, use the Pythagorean Theorem: c² = a² + b², or rearranged as a² = c² - b² or b² = c² - a².

Front

If one leg of a right triangle is 12 and the hypotenuse is 13, what is the length of the other leg?

Back

Using the Pythagorean Theorem: a² = 13² - 12² = 169 - 144 = 25. Therefore, the other leg is √25 = 5.

Front

What does it mean if a set of three numbers does not satisfy the Pythagorean Theorem?

Back

If a set of three numbers does not satisfy the equation a² + b² = c², they cannot form a right triangle.

Front

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

Back

Using the Pythagorean Theorem: a² = 15² - 9² = 225 - 81 = 144. Therefore, the other leg is √144 = 12.

Front

What is the relationship between the legs and the hypotenuse in a right triangle?

Back

The hypotenuse is always longer than either leg in a right triangle.