Question

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

Answer 1

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 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

Answer 2

Step-by-step explanation:

in the figure

△DCE and BFE

any DEC = any BEF (vertically opp any)

EC=BE (E is the mid point)

∠DCB=∠EBF (alternate angle DC parallel to AF)

So △DCE congruent to △BFE

Therefore DC=BF ...(1)

now CD = AB (ABCD is a parallelogram)

so AF=AB+BF

=AB+DC from (1)

=AB+AB

=2AB