Question

D and F are midpoints of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E.

1. Prove that BDFE is a parallelogram
2.  Find AB, if EF = 4.8 cm.

Answer 1

The required figure is shown below

(i) Since F is the midpoint and EF || AB.

Therefore E is the midpoint of BC.

So, `BE = 1/2BC and EF = 1/2AB`   …..(1)

Since D and F are the mid-points of AB and AC

Therefore DE || AC.

So, `DF = 1/2BC and DB = 1/2"AB"`  …..(2)

From (1), (2) we get

BE = DF and BD = EF

Hence  BDEF is a parallelogram.

(ii) Since

AB = 2EF

= 2 × 4.8

= 9.6 cm.