Question

In the triangle ABC fique AB=AC, BO and CO are the bisectors of angle ABC and angle ACB respectively. Prope that AO is the bisector of angle BAC ​

Answer 1

Answer:

in triangle AOB and triangle AOC

AB=AC(given)

angle ABO=Angle ACO(BO and CO are bisectors of angle ABC and angle ACB)

[in triangle BOC, angle OBC=angle OCB as angle ABC and angle ACB are bisectors

therefore,OB=OC-sides equal to opposite angles are equal]

OB=OC(proved above)

by SAS congruency,

triangle AOB is congruent to triangle AOC

By CPCT

angle OAB= angle OAC

hence AO is the bisector of angle BAC..

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