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). Formula: a² + b² = c².

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula for finding the hypotenuse is a² + b² = c².

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

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (a and b) and the hypotenuse (c).

Front

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

Back

8 cm (Using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64; √64 = 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

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

If a rectangular field is 40 yards wide and 30 yards long, how far is it across diagonally?

Back

50 yards (Using the Pythagorean Theorem: 40² + 30² = 1600 + 900 = 2500; √2500 = 50).

Front

What is the first step in using the Pythagorean Theorem to find a missing side?

Back

Identify which sides are known (the legs or the hypotenuse) and write down the Pythagorean equation.

Front

If a right triangle has legs of lengths 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).