Pythagorean Theorem and Special Right Triangles

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

In a 45-45-90 triangle, what is the relationship between the lengths of the legs?

Back

The lengths of the legs are equal.

Front

What is the length of the hypotenuse in a 45-45-90 triangle if each leg is of length 'x'?

Back

The length of the hypotenuse is x√2.

Front

In a 30-60-90 triangle, what is the relationship between the lengths of the sides?

Back

The length of the side opposite the 30° angle is half the length of the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the side opposite the 30° angle.

Front

What is the length of the hypotenuse in a 30-60-90 triangle if the shorter leg is 'x'?

Back

The length of the hypotenuse is 2x.

Front

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 'x'?

Back

The length of the longer leg is x√3.

Front

What is the formula used to solve for the hypotenuse in a right triangle?

Back

a² + b² = c².

Front

If one leg of a right triangle is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

10 (using the Pythagorean Theorem: 6² + 8² = c² => 36 + 64 = 100 => c = 10).

Front

What is the value of 'x' in a 30-60-90 triangle if the shorter leg is 3?

Back

The longer leg is 3√3 and the hypotenuse is 6.

Front

How do you find the area of a right triangle?

Back

Area = 1/2 * base * height.