Through the mid-point M 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.
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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.
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