Before the proof is presented, it is important that the next figure is explored since it directly relates to the proof. In this Pythagorean configuration, the square on the hypotenuse has been divided into 4 right triangles and 1 square, MNPQ, in the center. Each side of square MNPQ has length of a - b. As mentioned above, this proof of the Pythagorean Theorem can be further explored and proved using puzzles that are made from the Pythagorean configuration. Students can make these puzzles and then use the pieces from squares on the legs of the right triangle to cover the square on the hypotenuse.
Students can then use the puzzle to prove the Pythagorean Theorem on their own.
Figure 17 To create this puzzle, copy the square on BC twice, once placed below the square on AC and once to the right of the square on AC as shown in Figure 17. Triangle EGH is congruent to triangle ACB by leg-leg. Thus the diagonals CE and EH are both equal to c. The proofs presented here are just a few of the many proofs of the Pythagorean Theorem. The Pythagorean Theorem is a very important concept for students to learn and to understand.