Chapter 4.4, Problem 2CE

To determine

To Fill: The blank that if $\Delta BOC$ is isosceles, with $\overline{OB}=\overline{OC}$ , then $\angle \mathrm{....}\cong \angle \mathrm{....}$

Answer to Problem 2CE

The congruent angles are $\angle C\cong \angle B$ .

Explanation of Solution

Given information:

The figure where $\overline{OB}=\overline{OC}$

  

Concept and Formula Used:

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

Calculation:

It is given that $\overline{OB}=\overline{OC}$ and figure

  

The angle opposite to side $\overline{OB}$ is $\angle C$ and to side $\overline{OC}$ is $\angle B$ in $\Delta BOC$

According to theorem that if two sides of a triangle are congruent, then the angles opposite to those sides are congruent.

Therefore

  $\angle C\cong \angle B$

Conclusion:

The congruent angles are $\angle C\cong \angle B$ .