The Proof


The wording and proof of the Pythagorean Theorem can cause difficulties for students when learning geometry. A deep level of understanding is crucial.

With younger children, we have them illustrate the theorem as follows: On each side of a right triangle, draw a square with that side of the triangle as one edge of the square. Find the area of the three squares. We see that the sum of the areas of the smaller squares equals the are of the large square. This is often thought of as a proof, but it is not, it does not explain why the relationship is true for any right triangle.


The first proof we can recreate with SketchUp uses the group, move, translate and rotate tools. Don't add labels until after you group and move the shapes!
ProofPT.png

One of the most common mistakes I have encountered over the years is when the theorem is used for any triangle. Note the stress in the wording below.

If a triangle is a right triangle with side measures a, b and c (the hypotenuse), then a^2 + b^2 = c^2.

Checked June, 2014