https://file.aiquickdraw.com/mathbot/file/17277012926463710ddz8.jpg

Let's go through the proof step-by-step using the given information from the image. The goal is to prove that ∠1 is congruent to ∠3.

Here’s how we can complete the proof:

### Given Information:
- ∠1 and ∠2 form a linear pair.
- m∠2 + m∠3 = 180°.

### Proof:
1. **Statement:** ∠1 and ∠2 form a linear pair.
   - **Reason:** Given.

2. **Statement:** ∠1 and ∠2 are supplementary.
   - **Reason:** Linear pairs are supplementary.

3. **Statement:** m∠2 + m∠3 = 180°.
   - **Reason:** Given.

4. **Statement:** ∠2 and ∠3 are supplementary.
   - **Reason:** Definition of supplementary angles (sum of their measures is 180°).

5. **Statement:** ∠1 ≅ ∠3.
   - **Reason:** Angles supplementary to the same angle are congruent.

### Conclusion:
By using the fact that both ∠1 and ∠3 are supplementary to ∠2, we conclude that ∠1 is congruent to ∠3.

Do you need further details or clarification? Here are 5 related questions to expand the understanding:

1. What is the definition of a linear pair?
2. Why are angles that form a linear pair always supplementary?
3. How can you use congruent angles in other geometric proofs?
4. How would you prove two angles are supplementary if no measures are provided?
5. Can you use a different method to prove ∠1 ≅ ∠3?

**Tip:** Always pay attention to how angles are related (e.g., supplementary, complementary, vertical) to identify congruencies or equalities.

Complete the proof. Given ∠1 and ∠2 form a linear pair; m∠2 + m∠3 = 180. Prove: ∠1 ≅ ∠3.

Learn how to complete the proof showing that ∠1 ≅ ∠3, given ∠1 and ∠2 form a linear pair and m∠2 + m∠3 = 180°. This problem covers geometry concepts such as linear pairs, supplementary angles, and angle congruence. Suitable for Grades 8-10.

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