Pythagorean Theorem Basics

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 the hypotenuse in a right triangle?

Back

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

Front

If one leg of a right triangle measures 15, what is the hypotenuse?

Back

The hypotenuse cannot be determined with only one leg's length; additional information is needed.

Front

What type of triangle does the Pythagorean theorem apply to?

Back

The Pythagorean theorem applies only to right triangles.

Front

What is a leg in a right triangle?

Back

A leg is one of the two sides that form the right angle in a right triangle.

Front

If the lengths of the legs of a right triangle are 9 and 12, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 9² + 12²; c² = 81 + 144; c² = 225; c = 15.

Front

What is the relationship between the angles and sides in a right triangle?

Back

In a right triangle, the side opposite the right angle is the hypotenuse, and the other two sides are the legs, which form a right angle.

Front

If the hypotenuse is 36 and one leg is 30, what is the length of the other leg?

Back

Using the Pythagorean theorem: a² + 30² = 36²; a² + 900 = 1296; a² = 396; a ≈ 19.9.

Front

What is an acute angle?

Back

An acute angle is an angle that measures less than 90 degrees.

Front

What is an obtuse angle?

Back

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.