In the adjoining figure , ABC is an isosceles triangle. BO and CO are the bisectors of ABC and ACB respectively. Prove that BOC is an isosceles triangle.

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Here it's given that ∆ABC is a isosceles triangle. We know that in a isosceles triangle opposite angles are equal. And the angles opposite to equal sides are also equal.

Hence here ,

Figure :-

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Here we will use a theorem which is ,

Hence here,

Now in ∆OBC , we can see that ∠OBC = ∠OCB. (just proved ) . Hence we can say that sides OB and OC are equal. Since the sides opposite to equal angles are equal. Therefore in ∆OBC , two sides are equal.

Therefore ∆ OBC is an isosceles triangle.

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