Problem
Example Complete the proof by writing the missing reasons. Choose from the following reasons. You may use a reason more than once. Refer to the reason bank below. Given: $p \| q$ (line $p$ parallel to line $q$ ) Prove: $m \angle 3=m \angle 5$ Two-Column Proof of the Alternate Interior Angles Theorem
Solution
Step 1 ：Given that line p is parallel to line q, we can assume that a transversal line cuts the parallel lines p and q, forming the angles. Angle 3 and angle 5 are alternate interior angles.
Step 2 ：According to the Alternate Interior Angles Theorem, if two parallel lines are cut by a transversal, then the alternate interior angles are congruent.
Step 3 ：Therefore, \(m \angle 3=m \angle 5\).
Step 4 ：\(\boxed{m \angle 3=m \angle 5}\)
