Question

M is the mid-point of the side CD of a parallelogram. ABCD. The line BM is drawn intersecting AC at L and AD produced at E. Prove that EL=2BL.

Answer 1

see diagram.

we know MC = MD 

ΔBCM and ΔEDM are similar triangles, as sides are all parallel to corresponding sides.  Also MC = MD.  So triangles are congruent.
   =>  AD = BC = DE     => AE = 2 BC

ΔBCL and ΔAEL are similar triangles, as corresponding sides are parallel.
  => EL / BL = AE / BC = 2 
=>  EL = 2 BL  proved.

Answer 2

Your answer is given above.

Hope you find it helpful.