```EMAT 4680
In Class Midterm Exam
Fall 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)