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). It can be expressed as a² + b² = c².

Front

What is a right triangle?

Back

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

Front

What are the sides of a right triangle called?

Back

The sides of a right triangle are called the legs (the two shorter sides) and the hypotenuse (the longest side opposite the right angle).

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b²; c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

Which set of sides can form a right triangle? 5, 12, 13 or 4, 5, 6?

Back

5, 12, 13 can form a right triangle because 5² + 12² = 13².

Front

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

Back

c = √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

How do you find the length of one side of a right triangle if you know the other two sides?

Back

Use the Pythagorean Theorem: a² + b² = c². Rearrange to find the missing side.

Front

What is the distance from the top of a ladder to the base of the wall if the ladder is 10 feet long and the base is 4 feet from the wall?

Back

Using the Pythagorean Theorem: c = √(10² - 4²) = √(100 - 16) = √84 ≈ 9 feet.

Front

If a TV is advertised as 36 inches diagonal and measures 30 inches in length, how do you find the height?

Back

Use the Pythagorean Theorem: height = √(36² - 30²) = √(1296 - 900) = √396 ≈ 19.9 inches.

Front

What is the formula to calculate the area of a right triangle?

Back

Area = (1/2) * base * height.