Through the midpoint of M of the side CD of a parallelogram ABCD,the line BM is drawn intersecting AC in L and AD produced in E.prove that EL=2BL
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In △ BMC and △ EMD
∠ BMC = ∠ EMD [Vertically opposite]
MC = DM [Given]
∠ BCM = ∠ EDM [Alternate angles]
∴△BMC ≅ △EMD [By ASA]
Hence, BC = DE [By CPCT] →(1)
AE = AD+DE = BC + BC = 2BC →(2)
Now, △BLC ∼ △ELA (AA Similarly)
BL / EL = BC / AE (By CPCT) BL / EL = BC / 2BC
BL / EL = 1 / 2
EL = 2 BL
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