8.7C 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

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

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

Back

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

Front

What is the square root of a number?

Back

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4, because 4 x 4 = 16.

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is taking the square root of that number.

Front

In a right triangle, if one side is 5 inches and the hypotenuse is 13 inches, what is the length of the other side?

Back

Using the Pythagorean Theorem: a = √(c² - b²) = √(13² - 5²) = √(169 - 25) = √144 = 12 inches.

Front

What is a right triangle?

Back

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

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.

Front

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

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10 inches.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula is used to find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).