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: c² = a² + b².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) in a right triangle is: c = √(a² + b²).

Front

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

Back

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

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. The side opposite the 30° angle is the shortest.

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 length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

To find the length of a missing side, use the Pythagorean Theorem: c² = a² + b². Rearrange the formula to solve for the missing side.

Front

Casey travels 30 miles west and 40 miles north. How far does she travel home directly?

Back

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

Front

What is the diagonal length of a rectangle with width 6 and length 8?

Back

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

Front

If a right triangle has legs of lengths 5 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(5² + 12²) = √(25 + 144) = √169 = 13.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance formula between two points (x₁, y₁) and (x₂, y₂) is: d = √((x₂ - x₁)² + (y₂ - y₁)²).