### EMAT 6680 Final Project, Fall 2003

INSTRUCTIONS:

Complete each of the following parts. Part
One
is merely finishing off the write-ups for the semester. Part
Two
should be a new web page item. Part Three is the course evaluation.

Part One
**Review your Write-ups 1 to 12. Revise as
you wish to reach the point where you feel that, collectively,
the 12 write-ups represent your best work for the course. They
are an elctronic portofolio of your work.**

**Part ****Two**
**Complete a Write-up on your
Web Page for the following investigation. This should be individual
work.**

**A**. Consider any triangle ABC. Select
a point P inside the triangle and draw lines AP, BP, and CP extended
to their intersections with the opposite sides in points D, E,
and F respectively.

Explore (AF)(BD)(EC) and (FB)(DC)(EA)
for various triangles and various locations of P.

**B**. Conjecture? **Prove it!** (you
may need draw some parallel lines to produce some similar triangles)
Also, it probably helps to consider the ratio

Can the result be generalized
(using lines rather than segments to construct ABC) so that point
P can be **outside** the triangle? Show a working GSP sketch.

**C**. Show that when P is inside triangle
ABC, the ratio of the areas of triangle ABC and triangle DEF
is always greater than or equal to 4. When is it equal to 4?

**Part Three**

Return to **EMAT
6680 Home Page**.