# The Final Project

## Extensions

### Now that you have examined the above extensions see if you can discover Varignon's Theorem and write a GSP explanation.

1) Construct a trapezoid ABCD.

2) Find and label the midpoints of each side in order AB, BC, CD, and DA.

3) Define EFGH as a shape. (If any, what kind of quadrilateral does EFGH appear to be? It may require some measurements).

4) Using GSP to justify your conjecture. Explain in writing what you did to justify the conjecture.

5) Make a new sketch and construct your own quadrilateral. Again, find the midpoints of each side of your new quadrilateral and define this figure. Investigate this quadrilateral as you did above.

6) Have you discovered Varignon's Theorem?

If not, checkout the following website: The Theorem.

Other topics of interest to geometrical studies that may be used in the classroom.

Points of Concurrency related to Triangles

Side Side Angle Congruence (GSP4.0)

Medial Triangles

Tangent Circles and Loci

Constructing a Nine Point Circle

Pedal Triangle