https://file.aiquickdraw.com/mathbot/file/1727355342435qsag943f.jpg

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.

The proof shows that corresponding angles are congruent when two parallel lines are cut by a transversal. What is the missing statement in Step 2, and what is the missing reason in Step 3?

Understand how to prove that corresponding angles are congruent when parallel lines are cut by a transversal. Learn about the Vertical Angle Theorem, Corresponding Angles Postulate, and the Transitive Property in this step-by-step geometry proof. Suitable for students in Grades 8-10.

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