Question

State the theorem that justifies the statement∠6≅∠7.

The diagram,

Short answer

The theorem that justifies$\angle 6\cong \angle 7$is vertically opposite angles are always equal.

Step-by-step solution

Step 1. Define vertical angles.

When two lines intersect each other, four angles are formed. Two angles that are opposite to each other are called vertical angles and these angles are always equal.

Step 2. Observe the diagram.

From the diagram, it can be concluded that ∠6 and ∠7 are vertical angles.

Step 3. State the conclusion.

Since, vertical angles are always equal.

Therefore, the theorem that justifies $\angle 6\cong \angle 7$is vertically opposite angles are always equal.