# If the bisector o

Given in Δ ABC, AD bisects the A meeting BC at D

Construction:- Extend BA to E and join C to E such CE AD……… 4

BAD = AEC (corresponding s)……………… 2

CAD = ACE (alternate interior s)……………….. 3

From 1 , 2 and 3

ACE = AEC

In Δ AEC

ACE = AEC

AC = AE (sides opposite to equal angles are equal)……….. 5

In Δ BEC

And D is midpoint of BC (given)

By converse of midpoint theorem

A line drawn from the midpoint of a side, parallel to the opposite side of the triangle meets the third side in its middle and is half of it

A is midpoint of BE

BA = AE……… 6

From 5 and 6

AB = BC

ΔABC is an isosceles triangle

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