Creation of this applet was inspired by a [url=https://twitter.com/mburnsmath/status/824405871140577280]tweet[/url] from [url=https://twitter.com/mburnsmath]Marilyn Burns[/url] that was [url=https://twitter.com/ddmeyer/status/824409648866275328]retweeted[/url] by [url=https://twitter.com/ddmeyer]Dan Meyer[/url]. [br][br][color=#980000]Suppose a rectangle has a length that is twice its width. A diagonal is drawn from one vertex to the opposite vertex. In addition, 2 segments are drawn from one endpoint of this diagonal to the midpoints of the sides of the rectangle not adjacent that vertex. [/color][br][br][b]These 3 segments cause the rectangle to be split into 4 triangles of equal area. [br][/b][br]Feel free to change the size of the rectangle by moving the BIG WHITE POINT at any time.

[b]How do the dynamics of this applet informally suggest these 4 triangles have equal area? [/b][br][br][i][color=#0000ff]How can you formally prove what this applet informally illustrates? [/color][/i]