In Fig. 14.36, 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.

Question

Philoid · Accepted 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)