Parallelogram: Theorem 1

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 quadrilateral? Be specific!


Write a 2-column, paragraph, or coordinate geometry proof of what you've informally observed here. (Hint: If you choose a 2-column or paragraph proof, this proof will involve a pair of congruent triangles!)

Quick Demo: 0:00 sec to 0:33 sec (BGM: Andy Hunter)