∠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. 
 

**Given:**∠1∠1and ∠2∠2 are supplementary
**Prove:**∠1∠1and ∠3∠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 work through the proof, filling in the missing statements and justifications step by step:

### Proof:
---

**Given:**  
∠1 and ∠2 are supplementary  
∠1 ≅ ∠3  
m∠2 + m∠3 = 180

**To Prove:**  
∠1 ≅ ∠3

---

### Statements and Reasons:

1. **Statement:** ∠1 and ∠2 are supplementary  
   **Reason:** Given

2. **Statement:** *m*∠1 + *m*∠2 = 180  
   **Reason:** Supplementary angles add up to 180.

3. **Statement:** ∠2 and ∠3 are supplementary  
   **Reason:** Given

4. **Statement:** *m*∠2 + *m*∠3 = 180  
   **Reason:** Supplementary angles add up to 180.

5. **Statement:** *m*∠1 + *m*∠2 = *m*∠2 + *m*∠3  
   **Reason:** Transitive Property of Equality (since both equal 180)

6. **Statement:** *m*∠1 = *m*∠3  
   **Reason:** Subtraction Property of Equality (subtract *m*∠2 from both sides)

7. **Statement:** ∠1 ≅ ∠3  
   **Reason:** Angles with the same measures are congruent (Definition of congruent angles).

---

### Completed Proof:

1. **∠1 and ∠2 are supplementary** - *Given*  
2. **m∠1 + m∠2 = 180** - *Supplementary angles add up to 180*  
3. **∠2 and ∠3 are supplementary** - *Given*  
4. **m∠2 + m∠3 = 180** - *Supplementary angles add up to 180*  
5. **m∠1 + m∠2 = m∠2 + m∠3** - *Transitive Property of Equality*  
6. **m∠1 = m∠3** - *Subtraction Property of Equality*  
7. **∠1 ≅ ∠3** - *Angles with the same measures are congruent*

---

Would you like further details on any part of the proof? Here are some related questions to deepen your understanding:

1. Why do supplementary angles add up to 180 degrees?
2. What is the Transitive Property of Equality?
3. How does the Subtraction Property of Equality work in geometry?
4. What is the definition of congruent angles?
5. How can this proof be applied in other geometric situations?

**Tip:** Always make sure to clearly define relationships like "supplementary" and "congruent" when working through proofs.

∠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. Given: ∠1 and ∠2 are supplementary. Prove: ∠1 ≅ ∠3.

Learn how to prove that ∠1 ≅ ∠3 through supplementary angles and key properties such as the Transitive and Subtraction Properties of Equality. This detailed proof covers geometric concepts relevant to students in Grades 8-10.

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