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 are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are typically referred to as 'a' and 'b' in the Pythagorean Theorem.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

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 can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length is equal to the sum of the squares of the other two lengths (c² = a² + b²).

Front

What is a right angle?

Back

A right angle is an angle that measures exactly 90 degrees.

Front

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

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the lengths of the sides is defined by the Pythagorean Theorem: c² = a² + b².

Front

Can a triangle with sides 15, 12, and 9 be classified as a right triangle?

Back

Yes, because 15² = 12² + 9² (225 = 144 + 81).

Front

What is the formula to 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, rearranging as needed to solve for the unknown side.