# Quad Midpoints Action!

- Author:
- Tim Brzezinski

- Topic:
- Parallelogram, Quadrilaterals

In the applet below, a quadrilateral is shown.
You can move the vertices of this quadrilateral wherever you'd like.
Interact with this applet for a few minutes, then answer the questions appear below it.
Be sure to change the locations of the quadrilateral's vertices each time

*before*and*after*re-sliding the slider!**Questions:**1) How do you know the

**smaller white points**are

**midpoints**? Explain. 2) Notice how the

**midpoints of the sides**of this quadrilateral form

**vertices**of yet

**another quadrilateral**. How would you classify this

**quadrilateral**? That is, what would be the

**most specific name**you'd give this

**quadrilateral**? 3) What observation(s), in the applet above, prompted you to give the

**classification**you did for (2)? Explain fully why/how this applet informally suggests that your

**answer to (2)**is correct. 4) Formally prove that the

**midpoints of the sides**of

*any quadrilateral*always form

**vertices**of this type of

**specific quadrilateral**. Prove this using the format of a 2-column or paragraph proof. (If you need a hint getting started, refer to this worksheet.) 5) Use coordinate geometry to formally prove your response to (2) is true. (Hint: Place one vertex of this quadrilateral at (0,0). Place another vertex at (2a, 0).)