Question

In the adjacent figure ABCD is a parallellogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show That AF=2AB

Answer 1

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In the figure, 
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 AF)
 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
         = 2AB