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 is expressed as a² + b² = c².

Front

In a right triangle with sides of lengths 6, 8, and 10, which side is the hypotenuse?

Back

The hypotenuse is the longest side, which is 10.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

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

Back

Using the Pythagorean Theorem: c² = 5² + 12² = 25 + 144 = 169, so c = √169 = 13.

Front

What is the formula to find the length of a side in a right triangle using the Pythagorean Theorem?

Back

The formula is a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If one side of a right triangle is 9 and the hypotenuse is 15, how do you find the length of the other side?

Back

Use the Pythagorean Theorem: c² = a² + b². Here, 15² = 9² + b², so 225 = 81 + b², thus b² = 144, and b = 12.

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Is the statement 'a² - b² = c²' true for right triangles?

Back

No, that statement is false. The correct formula is a² + b² = c².

Front

What is the first step in using the Pythagorean Theorem to solve for a missing side?

Back

Identify which sides are known and which side you need to find, then apply the formula a² + b² = c².

Front

How do you solve for c in the equation a² + b² = c²?

Back

To solve for c, rearrange the equation to c = √(a² + b²).