EMAT 4680In Class Midterm ExamFall 2000

**Part One - Let's do
a Proof** - **10pts**

Using Ceva's Theorem, prove that the medians of any triangle are concurrent (use GSP to do the construction and write your illustrated proof on your GSP Sketch)

**Part Two - Let's Make
a Script - 10pts**

Given the bases and an angle of an isosceles trapezoid, make a script that...

- Constructs the trapezoid
- Translates the trapezoid horizontally twice the distance of the long base
- Reflects this translated trapezoid over a line parallel to the bases so that the distance between the translated and the reflected trapezoid is twice the short base.

When your script is done playing, I should see something like this:

**Part Three - Let's
Explore Parallelograms - 30pts**

- Investigate the kind of quadrilateral formed by the angle bisectors of a parallelogram.
- What is the relationship of this quadrilateral to the type of original parallelogram?
- Justify any conjectures that you make
- Prove one of your conjectures. (bonus)