In   ABC, ray BD bisects  ABC and ray CE bisects  ACB. If seg AB seg AC then prove that ED || BC.

Given , In ABC ray BD bisects ABC .
AB/BC = AD/CD ………..(i) [Angle bisector theorem]
Since ray CE bisects ACB
AC/BC = AE/BE …………….(ii) [Angle bisector theorem]
Given seg AB = seg AC.
Substitute AB in (ii)
AB/BC = AE/BE…..(iii)
From (i) AD/CD = AE/BE [in (i) AB/BC = AD/CD]
EDBC [ converse of basic proportionality theorem]
Hence proved.