Question

If$\mathrm{\Delta }AOD$ is isosceles, with $\overline{OA}\cong \overline{OD}$. Then$\angle \_\_\cong \angle \_\_$?

Short answer

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

Step-by-step solution

Step 1. Consider the figure.

Consider the figure.

Step 2. Apply the concept of isosceles triangles.

Property of isosceles triangle 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, the angle opposite to side$\overline{OA}$ is$\angle D$ and to side$\overline{OD}$ is$\angle A$ in $\mathrm{\Delta }AOD$.

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

Therefore the congruent angles are $\angle D\cong \angle A$.