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 can be expressed as: a² + b² = c².

Front

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

Back

5 feet (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a and b are the legs.

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

In a right triangle, if one leg is 6 inches and the hypotenuse is 10 inches, what is the length of the other leg?

Back

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

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

If a ladder is 15 feet long and is placed 9 feet from the wall, how high does it reach?

Back

12 feet (Using the Pythagorean Theorem: 9² + h² = 15²; 81 + h² = 225; h² = 144; h = 12).

Front

What is a right triangle?

Back

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

Front

If the legs of a right triangle are 5 cm and 12 cm, what is the length of the hypotenuse?

Back

13 cm (Using the Pythagorean Theorem: 5² + 12² = 25 + 144 = 169; √169 = 13).

Front

What is the formula to calculate the distance between two points in a coordinate plane?

Back

The distance formula is: d = √((x2 - x1)² + (y2 - y1)²).