Question

Through the mid point m of the side cd of a parallogram abcd, the line bm is drawn intersecting ac in l and ad produced on e. Prove that el=2 bl

Answer 1

Hi! Here is the proof to your question. Given: ABCD is a parallelogram where M is the midpoint of side CD. BM is drawn intersecting diagonal AC in Land AD produced in E. To prove: EL = 2BL

Proof: In ∆DME and ∆CMB EDM = BCM (pair of alternate angles) DM = CM (M is the midpoint of CD) DME = BMC (vertically opposite angles) ∴∆DME ≅ ∆CMB (ASA congruence criterion) ⇒ DE = BC (c. p. c. t) Now, In ∆ALE and ∆BLC, ALE = BLC (vertically opposite angles) AEL = LBC (pair of alternate angles) ∴∆ALE ∼ ∆CLB (AA similarity criterion)

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now see picture

Answer 2

Your answer is given above.

Hope you find it helpful.