Quadrilateral ABCD is a quadrilateral shown below. (Vertices are BIG.)
E, F, G, and H are midpoints of the sides of quadrilateral ABCD. (See figure.)
Quadrilateral EFGH is another quadrilateral whose vertices are the midpoints of the sides of quadrilateral ABCD.
Move each one of the BIG vertices of quadrilateral ABCD around. As you do, pay attention to the quadrilateral EFGH.
After interacting with this applet for a few minutes, please answer the questions that appear below it.

Questions:
1) How would you classify quadrilateral EFGH, regardless of where A, B, C, and D lie?
2) Use the tools of GeoGebra to prove your assertion is true.
3) Provide a formal, 2-column proof to prove your assertion true.
(Hint: Think of the Triangle-Midsegment Theorem we've just recently learned!)
4) Provide a coordinate geometry proof to prove your assertion true.