Pythagorean Theorem Review

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

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem applies only to right triangles.

Front

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

Back

Using the Pythagorean Theorem: c² = 6² + 8² = 36 + 64 = 100, so c = √100 = 10 cm.

Front

What is the formula for finding the length of a missing 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

What is the opposite operation of squaring a number?

Back

The opposite operation of squaring a number is taking the square root.

Front

If the hypotenuse of a right triangle is 13 cm and one side is 5 cm, how do you find the length of the other side?

Back

Use the Pythagorean Theorem: c² = a² + b². Here, 13² = 5² + b², so 169 = 25 + b², thus b² = 144, and b = √144 = 12 cm.

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 + b³ = c⁴' a correct representation of the Pythagorean Theorem?

Back

No, the correct representation is a² + b² = c².

Front

What is a right triangle?

Back

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

Front

How can you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.