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

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 side of a right triangle if you know the lengths of the other two sides?

Back

Use the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) and b = √(c² - a²) for the legs.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

It applies to right triangles, which have one angle measuring 90 degrees.

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

Back

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

Front

What is the area of a right triangle with legs of length 5 feet and 12 feet?

Back

30 square feet (Area = 1/2 * base * height = 1/2 * 5 * 12).

Front

What is the formula to find the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is a right angle?

Back

A right angle is an angle that measures exactly 90 degrees.