To wrap up this series of Pythagorean Problems of the Week, here is one that often presents difficulties for students at first. Where are the numbers?! What is the length of a side that is only assigned a letter!!?

There has been a purposeful flow to our weekly Pythagorean problems. We began with whole number measurements and solutions, the second one using the information to solve another problem, and moved to whole number measurements with an irrational number solution. We now end with a problem that preserves complete generality.

Can you use the “measurements” in these two pictures to prove that a2 + b2 = c2 is true for all right triangles? The length of “a” is the same in both figures, as is the length of “b” and “c.” For this problem, all corners that look square are square. The solution will be posted next week with a special tribute to the scarecrow from the Wizard of Oz.