Let's break down the proof given in the image:

Part A: Missing statement in Step 2

Step 2 should involve recognizing the congruency of vertical angles. In the diagram, $\angle 2$ and $\angle 5$ are vertical angles, and by the vertical angle theorem, vertical angles are congruent.

Thus, the missing statement in Step 2 is:

• $\angle 2 \cong \angle 5$

Part B: Missing reason in Step 3

Step 3 states that $\angle 4 \cong \angle 5$, which follows from the fact that angles $\angle 4$ and $\angle 2$ are corresponding angles, and since $\angle 2 \cong \angle 5$ (from Step 2), by the corresponding angles postulate (since lines $a$ and $b$ are parallel), the two angles must be congruent.

Thus, the missing reason in Step 3 is:

• Corresponding angles postulate

Final Answers:

• Part A (Missing Statement in Step 2): $\angle 2 \cong \angle 5$
• Part B (Missing Reason in Step 3): Corresponding angles postulate

Would you like further details on this proof? Here are some related questions you might find useful:

1. What is the vertical angle theorem?
2. Why are corresponding angles congruent when lines are parallel?
3. How do we use the transitive property in geometry?
4. Can the corresponding angles postulate be applied to non-parallel lines?
5. What is the converse of the corresponding angles postulate?

Tip: When working on angle congruence proofs, always consider using properties like vertical angles, corresponding angles, or alternate interior angles depending on the configuration of the lines.