Chapter 4.4, Problem 1CE

To determine

To Fill: The blank that if $\Delta AOD$ is isosceles, with $\overline{OA}=\overline{OD}$ , then $\angle \mathrm{....}\cong \angle \mathrm{....}$

Answer to Problem 1CE

The congruent angles are $\angle D\cong \angle A$ .

Explanation of Solution

Given information:

The figure where $\overline{OA}=\overline{OD}$

  

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 $\overline{OA}=\overline{OD}$ and figure

  

The angle opposite to side $\overline{OA}$ is $\angle D$ and to side $\overline{OD}$ is $\angle A$ in $\Delta AOD$

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

Therefore

  $\angle D\cong \angle A$

Conclusion:

The congruent angles are $\angle D\cong \angle A$ .