Parallelogram: Theorem (3)

Interact with the applet below for a few minutes. [br]Then, answer the questions that follow. [br][br]Feel free to move the BIG WHITE POINTS anywhere you'd like! [br][color=#ff00ff]You can also adjust the size of the pink angle by using the slider.[/color]
1.
What special type of quadrilateral was formed in the first half of your sliding-the-slider? How do you know this?
2.
What else can you conclude about this special type of parallelogram? Be specific!
3.
Write a coordinate geometry proof that formally proves what you've seen illustrated here. [br](Make sure you have appropriate variable coordinates for your initial setup!) [br][br]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)
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Information: Parallelogram: Theorem (3)