Parallelogram: Theorem (3)

Interact with the applet below for a few minutes. Then, answer the questions that follow. Feel free to move the BIG WHITE POINTS anywhere you'd like! You can also adjust the size of the pink angle by using the slider.


What special type of quadrilateral was formed in the first half of your sliding-the-slider? How do you know this?


What else can you conclude about this special type of parallelogram? Be specific!


Write a coordinate geometry proof that formally proves what you've seen illustrated here. (Make sure you have appropriate variable coordinates for your initial setup!) For this theorem, a coordinate-geometry method of proof is actually A LOT EASIER than a 2-column or paragraph proof!

Quick Demo: 1:16 sec to END (BGM: Andy Hunter)