Question

Complete.

$\angle AOB\cong \underset{¯}{?}$

Short answer

The complete statement is: $\angle AOB\cong \angle EOD$.

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.

The theorem 2-3 states that the vertical angles are congruent.

Step 4. Write the relations between the angles AOB and EOD.

From the diagram, it can be noticed that:

The angles $AOB$and $EOD$are vertically opposite angles.

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

Step 5. Complete the statement.

As, the angles $AOB$and $EOD$are congruent angles.

Therefore, $\angle AOB\cong \angle EOD$.

Therefore, the complete statement is:$\angle AOB\cong \angle EOD$.