Question

Write the name or statement of the definition, postulate, or theorem that justifies the statement about the diagram.

$\angle 2\cong \angle 6$

Short answer

The name of the theorem which justifies the statement about the given diagram is vertical angle theorem.

Step-by-step solution

Step 1. Observe the given diagram.

The given diagram is:

Step 2. Write the vertical angle theorem.

The vertical angle theorem states that the vertical angles are congruent.

Step 3. Write the name of the theorem that justifies the statement about the given diagram.

From the given diagram it can be noticed that the angles∠2 and∠6are vertical angles, therefore the angles∠2 and∠6 are congruent by using the vertical angle theorem.

Therefore, the name of the theorem that justifies the statement about the given diagram is vertical angle theorem.