∠1 and ∠2 are supplementary∠1 ≅ ∠3m∠2 + m∠3 = 180m∠1 + m∠2 = m∠2 + m∠3m∠1 + m∠3m∠1 + m∠2 = 180
Complete the proof by selecting the correct justification for the statement. 
 
Given:∠1
and ∠2
 are supplementary
Prove:∠1
and ∠3



Fill-in the missing statements by moving the correct answer to the empty boxes. 
 
Statements	Reason
1. ∠1 and ∠2 are supplementary	1. Given
2. m∠1 + m∠2 = 180	2. Supplementary angles add up to 180.
3. ∠2 and ∠3 are supplementary	3. Given
4. 	4. Supplementary angles add up to 180.
5.  m∠1 + m∠2 = m∠2 + m∠3	5. Transitive Property of Equality
6. 	6.  Subtraction Proeprty of Equality
7. 	7. ∠’s with the same measures are ≅.

Let's fill in the missing steps of the proof and select the correct justifications for each statement.

### Statements and Reasons:
| **Statements**                        | **Reason**                                     |
|---------------------------------------|------------------------------------------------|
| 1. ∠1 and ∠2 are supplementary        | 1. Given                                       |
| 2. m∠1 + m∠2 = 180                    | 2. Supplementary angles add up to 180°          |
| 3. ∠2 and ∠3 are supplementary        | 3. Given                                       |
| 4. m∠2 + m∠3 = 180                    | 4. Supplementary angles add up to 180°          |
| 5. m∠1 + m∠2 = m∠2 + m∠3              | 5. Transitive Property of Equality              |
| 6. m∠1 = m∠3                          | 6. Subtraction Property of Equality             |
| 7. ∠1 ≅ ∠3                            | 7. ∠'s with the same measures are ≅             |

### Explanation:
1. **Step 1** states that ∠1 and ∠2 are supplementary, which is given.
2. **Step 2** uses the fact that supplementary angles add up to 180 degrees.
3. **Step 3** states that ∠2 and ∠3 are supplementary, which is also given.
4. **Step 4** uses the same rule about supplementary angles adding up to 180 degrees.
5. **Step 5** uses the **Transitive Property of Equality**: if both sums (m∠1 + m∠2 and m∠2 + m∠3) equal 180, then they are equal to each other.
6. **Step 6** applies the **Subtraction Property of Equality**, subtracting m∠2 from both sides of the equation to get m∠1 = m∠3.
7. **Step 7** concludes that ∠1 ≅ ∠3 because angles with equal measures are congruent.

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### Related Questions:
1. What is the definition of supplementary angles?
2. How does the Transitive Property of Equality work in geometry?
3. Why is the Subtraction Property of Equality necessary in this proof?
4. What is the formal definition of congruent angles?
5. How can you prove angles are supplementary in other geometric scenarios?

**Tip:** Always write down your known facts and given information before trying to solve a proof—this helps to identify the necessary logical steps.

∠1 and ∠2 are supplementary ∠1 ≅ ∠3 m∠2 + m∠3 = 180 m∠1 + m∠2 = m∠2 + m∠3 m∠1 + m∠3 m∠1 + m∠2 = 180. Complete the proof by selecting the correct justification for the statement.

Explore the step-by-step proof involving supplementary and congruent angles. Learn about key geometry concepts such as the Transitive and Subtraction Properties of Equality, suitable for Grades 8-10.

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