through the midpoint m of the side cd of a paralelogram abcd,the line bm is drawn intersecting ac in l and ad produced in e.prove that el=2bl
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)
Al/cl=el/bl=ae/cb
El/bl=ae/bc
El/bl=ad+de/bc
El/bl=2bc/bc
El=2bl
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