Answer to Question #160026 in Geometry for jeffery

Question

D and E are any two points on the sides AB and AC respectively of the triangle ABC. DG drawn parallel to BE meets AC in G and EF drawn parallel to CD meets AB in F. Prove that F G is parallel to BC

Answer 1

To show that this is correct, note that angles ACB and BCA are congruent. Let the lines AB and CD intersect at E. Then angles AEB and CED are both straight and E are arbitrary points obituary along the two arms of the given angle of FE at D.

Through D, draw the DL parallel to FH and extend the GB and HA so they meet.