Question

Prove that any line segment drawn from a vertex of a triangle to a point on the opposite side is bisected by the segment joining the middle points of the other two sides

Answer 1

Answer:

Given that, ABC is a triangle

Let D be the mid point of AB and E be the midpoint of AC.

F be the mid point of BC then AF is the straight line that bisects DE at point O.

TO PROVE:- DE bisects AF

PROOF:- since D and E are the mid points of the side AB and AC respectively of ΔABC, then

DE∥BC ………. (1)

since DE∥BC, then DO∥BF [as BF be the part of BC and DO be the

part of DE]

In ΔABF, then we know that D is the mid point of AC and O be the mid point of AF.

Then, DO∥BF (by Converse of mid point theorem)

⇒ AO=OF

Hence, DE bisects AF.

Hence proved.