# Pythagorean Converse: Acute, Right, or Obtuse?

In the applet below, you'll see a triangle with a colored square built off each side. You can change the size and shape of this triangle by moving its BIG GRAY VERTICES around. You can also use the red slider. Interact with the applet below for a few minutes. Then, answer the questions that follow on a piece of paper. Notice the calculation being done for you in the top left corner!
Questions: 1) Is it at all possible for the sum of the areas of the 2 smaller squares to be EQUAL TO the area of the largest square? If this is possible, how would you classify such a triangle (for which you observe this to be true) by its angles? 2) Is it at all possible for the sum of the areas of the 2 smaller squares to be GREATER THAN the area of the largest square? If this is possible, how would you classify such a triangle (for which you observe this to be true) by its angles? ﻿3) Is it at all possible for the sum of the areas of the 2 smaller squares to be LESS THAN the area of the largest square? If this is possible, how would you classify such a triangle (for which you observe this to be true) by its angles?