Question

Complete.

$\angle AOE\cong \underset{¯}{?}$

Short answer

The complete statement is: $\angle AOE\cong \angle BOD$.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Definition of congruent angles.

The two angles are said to be congruent angles if they have equal measure.

If two angles A and B are congruent then it can be written as$\angle A\cong \angle B$.

Step 3. Write the theorem 2-3.

Theorem 2-3 states that the vertical angles are congruent.

Step 4. Write the relations between the angles AOE and BOD.

From the diagram, it can be noticed that:

The angles $AOE$and $BOD$are vertically opposite angles.

Therefore, from theorem 2-3, it can be said that the angles $AOE$and $BOD$are congruent angles.

Step 5. Complete the statement.

As the angles $AOE$and $BOD$are congruent angles.

Therefore, $\angle AOE\cong \angle BOD$.

Therefore, the complete statement is: $\angle AOE\cong \angle BOD$.