Let ABCDE be a convex pentagon such that the
triangles ABC, ACD, and ADE are similar.
The diagonals BD and CE intersect in point P.

Prove that the ray AP bisects side CD.

(In reply to re(5): Question? by Bractals)

Is the issue whether the three triangles are not only SIMILAR but are also CONGRUENT -- given that the pentagonal figure is convex (but perhaps not regular). Will the ray with A endpoint, and passing thru P,  necessarily bisect CD?  If so, will it only do so if the pentagon is regular?

Posted by ed bottemiller on 2010-10-18 18:17:34