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The problem asks you to complete a flow proof of the Converse of the Alternate Exterior Angles Theorem.

You are given that ∠1 ≅ ∠2, and need to prove that ∠2 ≅ ∠3. The appropriate justification for ∠2 ≅ ∠3 would be the **Vertical Angles Theorem**. This is because in the diagram, ∠2 and ∠3 are vertical angles, which are always congruent.

To summarize:
- ∠1 ≅ ∠2 is given.
- ∠2 ≅ ∠3 because of the **Vertical Angles Theorem**.

Would you like a deeper explanation of how vertical angles work, or any other part of the proof?

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Here are five questions to expand on the topic:
1. What is the Converse of the Alternate Exterior Angles Theorem?
2. How do you prove that alternate exterior angles are congruent when two lines are cut by a transversal?
3. What is the difference between a theorem and its converse?
4. What other types of angle theorems are used in geometry?
5. How can you use corresponding angles to prove parallel lines?

**Tip:** Vertical angles are always congruent, and they form when two lines intersect. This property is crucial in many geometric proofs!

Complete the flow proof of the Converse of the Alternate Exterior Angles Theorem, given that ∠1 ≅ ∠2, and determine the reason for ∠2 ≅ ∠3.

Learn how to complete a flow proof for the Converse of the Alternate Exterior Angles Theorem, given ∠1 ≅ ∠2. Understand the use of the Vertical Angles Theorem to justify why ∠2 ≅ ∠3 in this geometry problem, suitable for Grades 9-10.

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