Pythagorean Theorem/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

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

Identify a set of sides that can form a right triangle.

Back

The sides 5, 12, and 13 can form a right triangle.

Front

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 5?

Back

The length of the hypotenuse is 5√2.

Front

What is the formula to find the hypotenuse of a right triangle?

Back

The formula is a² + b² = c².

Front

In a 30-60-90 triangle, if the shorter leg is 5, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10.

Front

In a 30-60-90 triangle, if the hypotenuse is 12, what is the length of the shorter leg?

Back

The length of the shorter leg is 6.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

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

Back

The length of the hypotenuse is 5.

Front

What is the length of the longer leg in a 30-60-90 triangle if the shorter leg is 4?

Back

The length of the longer leg is 4√3.