Question

9: IF AB, CD, EF are three parallel lines intersected by two transversals i and m such that AC=CE.
Prove that BD=DF.

Answer 1

draw a line AF intersecting CD at G.

In triangle AEF

C is the m.p of AE & CG is parallel to EF

hence ,by m.p theorem G is the m.p of AF.

now,in triangle ABF

G is the m.p of AF & GD is parallel to AB.

hence,by m.p theorem D is the m.p of BF.

therefore,BD=DF