Review and revise writeups # 1 - 12.

A.Consider any triangleABC. Select a pointPinside the triangle and draw linesAP, BP,andCPextended to their intersections with the opposite sides in pointsD, E,andFrespectively. Explore(AF)(BD)(EC)and(FB)(DC)(EA)for various triangles and locations ofP.

B.Conjecture? Prove it! (You may need to 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

DABC) so that pointPcan be outside the triangle? Show a working GSP Sketch.

C.Show that whenPis in the triangle, the ratio of the areas ofD ABCandD DEFis always greater than or equal to 4. When is it equal to 4?Write-up