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 use the Pythagorean Theorem to find a missing leg
• how to use the Pythagorean theorem to find the length of a space diagonal in a rectangular prism
• how to use the converse of the Pythagorean Theorem
• how to use the Pythagorean Triples

Using the Pythagorean Theorem to find a Missing Leg

The legs of a right triangle are the sides that are adjacent to its right angle. Sometimes we have problems that ask us to find a missing length of one of these legs. We can use the Pythagorean theorem to find a missing leg of a triangle, but only if we know the length measure of the hypotenuse and the other one of the legs.

Common example - instead of finding out the length of the hypotenuse, we find the length of the leg of a right triangle

In this video, we use the Pythagorean theorem to find the length of a leg of a right triangle.

Space Diagonal

The Pythagorean theorem is useful when we need to find the length of a space diagonal in a rectangular prism. The space diagonal is the diagonal passing through the space between vertices, instead of the bases or lateral faces. In other words, it is the diagonal that joins two opposing vertices in the prism, or the two vertices that don't share a face with each other.

How to define and calculate a space diagonal.

Converse of the Pythagorean Theorem

If we know that the sum of two square sides in a triangle equals the square of the third side, we can conclude that the triangle is a right triangle. Pythagorean triples are commonly seen side lengths that indicate when a triangle is a right triangle. Knowing these triples will save time when in calculations related to the Pythagorean theorem.
How to use the converse of the Pythagorean Theorem to determine if a triangle is a right triangle, how to use Pythagorean triples to memorize the lengths of certain right triangles

This video shows how to use the Pythagorean Theorem and its Converse to determine if a triangle is acute, right, or obtuse.