# MP's of Quad Sides

- Author:
- Tim Brzezinski

- Topic:
- Parallelogram, Quadrilaterals

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.