Equilateral Triangle and Rectangle (Area Problem)

Creation of this applet was inspired by a tweet from Matthew Scroggs that was retweeted by Martin Gardner tweet. Interact with the applet for a few minutes. As you do, feel free to adjust the blue slider and the locations of the white points. Answer the questions that follow.


How do the dynamics illustrated above (informally) imply that the areas of the two smaller right triangles add to the area of the largest right triangle?


How can you formally prove what this applet informally illustrates?

Quick (Silent) Demo