From the previous page, use the Paragraph Proof of the Vertical Angles Theorem to write a two-column proof of the Vertical Angles Theorem. Refer to the reason bank below
Given: $\angle 1$ and $\angle 3$ are vertical angles
Prove: $\angle 1 \cong \angle 3$
Two-Column Proof of the Vertical Angles Theorem
Answer
Final Answer: \(\boxed{\angle 1 \cong \angle 3}\), which is the Vertical Angles Theorem
Step 1 ：Given: \(\angle 1\) and \(\angle 3\) are vertical angles
Step 2 ：Prove: \(\angle 1 \cong \angle 3\)
Step 3 ：Statements: \(\angle 1\) and \(\angle 2\) are supplementary, \(\angle 2\) and \(\angle 3\) are supplementary
Step 4 ：Reasons: Linear pair postulate, Linear pair postulate
Step 5 ：\(\angle 1 \cong \angle 3\) because if two angles are supplementary to the same angle, then they are congruent (Transitive Property of Equality)
Step 6 ：Final Answer: \(\boxed{\angle 1 \cong \angle 3}\), which is the Vertical Angles Theorem
