Question

In triangle ABC, angle B is obtuse. D and E are mid-points of sides AB and BC respectively and F is a point on side AC such that EF is parallel to AB. Show that BEFD is a parallelogram.

Answer 1

The figure is shown below

AD = DB

BE = EC

EF || BD

In Δ ABC

E is the midpoint of AB and 

EF || BD

∴ By the midpoint theorem, F will be the midpoint of AC and D will be the midpoint of AB.

As D and F are midpoints of AC and AB respectively.

∴ By the midpoint theorem of DF || BC or BE

Since DF || BE and EF || BD

Hence, BEFD is a parallelogram.