Fostering a Geometric Proof
You have been given a piece of paper measuring 8.5 inches by 11 inches. Fold the paper so the top right corner (point D) falls somewhere along the bottom edge of the paper as suggested by point F along edge BC in the following sketch.
Determine the maximum area of triangle EFC. What type of triangle is EFC in this case? Reflect EFC over the bottom edge of the paper (BC) to reveal a possible geometric proof.