91Ó°ÊÓ

The given diagram is:

It is being given that $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}$and $\stackrel{¯}{OB}â‰\dots \stackrel{¯}{OC}$.

In the triangles $\mathrm{Δ}AOB$and $\mathrm{Δ}AOC$, it can be noticed that:

$$\begin{gathered} \stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}\left(given\right) \\ \stackrel{¯}{OB}â‰\dots \stackrel{¯}{OC}\left(given\right) \\ \stackrel{¯}{AO}â‰\dots \stackrel{¯}{AO}\left(reflexiveproperty\right) \end{gathered}$$

Therefore, the triangles$\mathrm{Δ}AOB$ and$\mathrm{Δ}AOC$are the congruent triangles by using $SSS$postulate.

Therefore, by using the corresponding parts of congruent triangles it can be said that $∠AOBâ‰\dots ∠AOC$.

Yes, it is possible to prove that $∠AOBâ‰\dots ∠AOC$.

The given diagram is:

It is being given that $\stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}$and $\stackrel{¯}{OB}â‰\dots \stackrel{¯}{OC}$.

In the triangles $\mathrm{Δ}AOB$and role="math" localid="1648884343636" $\mathrm{Δ}AOC$, it can be noticed that:

$$\begin{gathered} \stackrel{¯}{AB}â‰\dots \stackrel{¯}{AC}\left(given\right) \\ \stackrel{¯}{OB}â‰\dots \stackrel{¯}{OC}\left(given\right) \\ \stackrel{¯}{AO}â‰\dots \stackrel{¯}{AO}\left(reflexiveproperty\right) \end{gathered}$$

Therefore, the triangles$\mathrm{Δ}AOB$ and$\mathrm{Δ}AOC$are the congruent triangles by using $SSS$postulate.

Therefore, by using the corresponding parts of congruent triangles it can be said that $∠AOBâ‰\dots ∠AOC$.

Therefore, the data is insufficient to prove that$∠AOB$ and$∠AOC$ are right angles.

No, it is not possible to prove that $∠AOB$and $∠AOC$are right angles.