In Class Midterm Exam
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
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
- Prove one of your conjectures.