Creation of this applet was inspired by a [url=https://twitter.com/gogeometry/status/944344444026880000]tweet[/url] from [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url] (GoGeometry). [br][br]Feel free to move the vertices of the quadrilateral anywhere you'd like. [br]Note: This applet works best if the quadrilateral is kept convex. [br][br][b][color=#0000ff]How can we formally prove the relationships dynamically illustrated here? [/color][/b]