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Pythagorean Theorem

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More Lessons for High School Geometry

More Lessons for Geometry

Math Worksheets

A series of free, online High School Geometry Video Lessons and solutions.
Videos, worksheets, and activities to help Geometry students.

In these lessons, we will learn

  • how to proof the Pythagorean Theorem
  • how to simplify square roots, which can be useful when working with the Pythagorean Theorem
  • how to use the Pythagorean Theorem to find a missing hypotenuse

Pythagorean Theorem Proofs

The Pythagorean theorem states that in a right triangle the sum of its squared legs equals the square of its hypotenuse. The Pythagorean theorem is one of the most well-known theorems in mathematics and is frequently used in Geometry proofs. There are many examples of Pythagorean theorem proofs in your Geometry book and on the Internet.

How to prove the Pythagorean Theorem using Algebra to show the area of the smaller square plus the area of four triangles is equal to the area of the larger square.

Proof of the Pythagorean Theorem using similarity.

Square Root Operations

Since Pythagorean theorem proofs requires us to square numbers and find square roots, reviewing square root operations from Algebra is really important. When working with the Pythagorean theorem, it is especially important for you to remember how to simplify square roots and rationalize fractions that have a square root in the denominator.
How to simplify square roots using two different methods.
The following video illustrates how to simplify square roots using perfect square factors.

Using the Pythagorean Theorem to find a Missing Hypotenuse or Missing Leg

The hypotenuse of a right triangle is the side that is opposite of its right angle. Sometimes we have problems that ask us to find the missing hypotenuse of a right triangle. We can use the Pythagorean theorem to find the hypotenuse, but only if we know the length measure of the two legs.
How to calculate the hypotenuse in a right triangle given the lengths of the legs using the Pythagorean Theorem.
In this video, we use the Pythagorean theorem to find the length of the missing leg of a right triangle.

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