# ABCD is a parallelogram and E is midpoint of side BC. If DE and AB are produced to meet at f,show that AF=2AB

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Δ DCE nd Δ BFE,

ang.DEC = ang. BEF ( vertically opp. ang.)

EC =BE ( E is the mid pnt)

ang. DCB =ang. EBF (alternate ang....... DC parallel ro AfF)

so ΔDCE congruent to Δ BFE

therefore DC = BF--------- (1)

now, CD = AB (ABCD is a parallelogram)

so AF = AB + BF

= AB + DC from (1)

= AB + AB

= 2 AB

hence proved............. hope dis helps