This is the write-up of the Final Assignment Brian R. Lawler EMAT 6680 12/16/00

## FINAL ASSIGNMENT

Part One

I have reviewed my Write-ups 1 - 12. I did some revising, spell checking, and link testing to the point I feel that, collectively, the 12 write-ups represent my best work for the time allotted during the course/semester. These write-ups stand as an electronic portfolio of my 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?