Pythagorean Theorem & Converse

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 legs of a right triangle?

Back

The legs of a right triangle are the two shorter sides that form the right angle.

Front

What is the hypotenuse of a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

How do you determine if a set of lengths can form a right triangle?

Back

To determine if a set of lengths can form a right triangle, check if the lengths satisfy the Pythagorean Theorem: a² + b² = c², where c is the longest length.

Front

If one leg of a right triangle is 12 and the other leg is 9, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 12² + 9² = 144 + 81 = 225. Therefore, c = √225 = 15.

Front

What is the area of a rectangle with a width of 15 inches and a length of 20 inches?

Back

The area of a rectangle is calculated as length × width. Therefore, Area = 20 × 15 = 300 in².

Front

If the diagonal of a rectangle is 25 inches and the width is 15 inches, what is the length?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 25² = length² + 15². Therefore, length² = 625 - 225 = 400, so length = √400 = 20 inches.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is calculated as: Area = 1/2 × base × height.

Front

How far from the base of a house do you need to place a 15' ladder to reach the top of a 12' wall?

Back

Using the Pythagorean Theorem: 15² = 12² + distance². Therefore, distance² = 225 - 144 = 81, so distance = √81 = 9 feet.