ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF = A. (3/2)AB B. 2 AB C. 3 AB D. (5/4)AB

Question

ABCD is a parallelogram and E is the mid-point of BC. DE and AB when produced meet at F. Then, AF = 

A. \(\frac{3}{2}\)AB 

B. 2AB 

C. 3AB 

D. \(\frac{5}{4}\)AB

Answer 1

Option : (B) 

ABCD is a parallelogram. 

E is the midpoint of BC. 

So, 

BE = CE 

DE produced meets the AB produced at F 

Consider the triangles CDE and BFE 

BE = CE (Given) 

∠CED = ∠BEF (Vertically opposite angles) 

∠DCE = ∠FBE (Alternate angles) 

Therefore, 

ΔCDE ≅ ΔBFE 

So, 

CD = BF (c.p.c.t) 

But, 

CD = AB 

Therefore, 

AB = BF 

AF = AB + BF 

AF = AB + AB 

AF = 2 AB