1.

In Fig,ABCD is a parallelogram and E is the mid-point of side BC. If DE and AB when produced meet at F, Prove that,AF = 2AB.

Answer»

Given, 

In a parallelgram ABCD, 

E = mid point of side BC

AD || BC

AD || BE

E is mid point of BC 

So, 

In ΔDEC and ΔBEF 

BE = EC .. (E is the mid point) 

∠DEC = ∠BEF 

∠DCB = ∠FBE 

(vertically opposite angles) 

So, 

ΔDEC ≅ ΔBEF 

DC = FB 

= AB + DC = FB + AB 

= 2AB = AF (proved)



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