Question

D,E and F are respectively the mid points of AB,BC and CA of a triangle ABC show that BEDF is a parallelogram​

Answer 1

Answer:

Step-by-step explanation:Given:ABC is a Triangle in which the midpoints of sides BC ,CA and AB are  D, E and F.

To show:(i) BDEF is a parallelogram. (ii) ar (DEF) = 1/4ar (ABC) (iii) ar (BDEF) =1/2 ar (ABC)

Proof: i)Since E and F are the midpoints of AC and AB.

BC||FE & FE= ½ BC= BD

(By mid point theorem)

BD || FE & BD= FE

Similarly, BF||DE & BF= DE

Hence, BDEF is a parallelogram

.[A pair of opposite sides are equal and parallel]