Criticize the following argument which proves that every triangle is isosceles. Consider triangle ABC (Fig. 9-17) and

Question:

Criticize the following argument which “proves” that every triangle is isosceles. Consider triangle ABC (Fig. 9-17) and let AD be the altitude from A to BC. Now let PQ be any parallel to BC and PR and QS parallel to AD. Then PR = QS. By drawing parallels such as PQ we can cover triangle BAD by lines such as PR. Similarly, we can cover triangle CAD by lines such as QS. Hence triangle BAD equals CAD and triangle ABC is isosceles.