By: Tim Lehman

With the area knowledge of our students after
Lesson 5, they are ready to prove the Pythagorean Theorem. The
Pythagorean Theorem is included at this time because of its importance
in mathematics and being needed for further area study. We feel
the Pythagorean Theorem is one of the most prominent topics in
high school mathematics. It should be presented early in a Geometry
course because of its power and necessity in future study. Because
using the area of squares offers a proof that can be visualized
and (with proper teacher prompts) constructed by the students,
we want the theorem in our curriculum during this unit. **Click here** for a GSP sketch for those
who doubt that the theorem holds. GSP can help students see more
definitely the proof of the theorem. Sample sketches from GSP's
Sample Sketches folder that can be found **here**
and **here** assist students with
this.

Another computer-generated proof of the theorem
by Jim Morey can be found **here**.

To have a deeper understanding of the Pythagorean
Theorem, students must understand how to use it. Therefore, applications
of the theorem should be included following its introduction.
Students can find perimeter of right triangles if given two sides
and other problems. The class needs to be able to solve problems
such as they might face later in life that could use the Pythagorean
Theorem. Common applications exist in the field of construction.
For example, it can be used to show that a room is square. **Or, to find how far a catcher throws
the ball when attempting to throw out a baserunner stealing second**.