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.