Q. 214.0( 13 Votes )

If the bisector o

Answer :


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


BD = DC and BAD = CAD…………. 1


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


AD CE (From .4)


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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