Question

In Fig. 9.20, D, E, F are the mid-points of BC, CA and AB respectively. Prove that AD bisects EF. ​

Answer 1

Step-by-step explanation:

Given:

D,E,F are mid-points of sides BC, CA and AB of a △ABC

To prove:

AD and FE bisect each other

Construction:

Join ED and FD

Proof:

By mid point theorem,

D and E are the midpoints of BC and AB

⇒DE∥AC⇒DE∥AF --- (1)

D and F are the midpoints of BC and AC

⇒DF∥AB⇒DF∥AE ---(2)

From (1) and (2),

ADEF is a parallelogram.

We know that,

The diagonals of a parallelogram bisect each other.

∴ AD and FE bisect each other.