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  • In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that : (ii) AO bisects ∠ A

1.(ii)  In an isosceles triangle ABC, with \small AB=AC, the bisectors of \small \angle B and \small \angle C intersect each other at O. Join A to O. Show that :

 (ii) AO bisects \small \angle A 

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Consider \Delta AOB  and  \Delta AOC,

(i)   AB\ =\ AC                  (Given)

(ii)   AO\ =\ AO            (Common in both the triangles)

(iii)   OB\ =\ OC          (Proved in previous part)

Thus by  SSS congruence rule, we can conclude that  :

                                      \Delta AOB\ \cong \ \Delta AOC

Now, by c.p.c.t., 

                                      \angle BAO\ =\ \angle CAO

Hence  AO bisects \angle A.

Posted by

Sanket Gandhi

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