Question

For the following figure, if $\mathrm{\Delta }BOC$is isosceles with $\overline{OB}\cong \overline{OC}$then$\angle \_\_\cong \angle \_\_$.

Short answer

Then$\angle C\cong \angle B$

Step-by-step solution

Step 1. Check the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangle.

Property of isosceles triangle states that if two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Step 3. Step description.

From the figure $\overline{OB}=\overline{OC}$.

Here the angle opposite to side$\overline{OB}$ is$\angle C$ and the angle opposite to side$\overline{OC}$ is$\angle B$ in $\mathrm{\Delta }BOC$.

Since if the two sides of a triangle are congruent then the angles opposite to those sides are congruent then $\angle C\cong \angle B$.

Therefore, the congruent angles are $\angle C\cong \angle B$.