Quad Midpoints Action!
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).)