Pythagoras in 3-D

Strategies and Hints

  1. Most students will probably write these four expressions:



  2. No, k is not needed in order to write this area. Encourage students to speculate as to why the altitude k is included in the drawing at all.
  1. In order to prove the theorem, the area of the bottom face must be written as rather than .

Solution

Students should start with an equation to prove written in the following form.

Next, the Pythagorean Theorem is used twice. Students should substitute for on the left side of the equation. Then, they should substitute for .