Question 1191305
Here's the completed proof with the corrected steps:

**Given:**

AB ≅ DC
M is the midpoint of AB.
N is the midpoint of DC.

**Prove:**

AM ≅ MB ≅ DN ≅ NC

| Statements | Reasons |
|---|---|
| 1. AB ≅ DC | 1. Given |
| 2. AB = DC | 2. If segments are ≅, then they are = in length. |
| 3. AM + MB = AB; DN + NC = DC | 3. Segment Addition Postulate |
| 4. AM + MB = DN + NC | 4. Substitution (since AB=DC) |
| 5. M is the midpoint of AB; N is the midpoint of DC. | 5. Given |
| 6. AM = MB and DN = NC | 6. The midpoint of a segment forms two segments = in measure. |
| 7. AM + AM = DN + DN | 7. Substitution (substituting MB for AM and NC for DN in step 4) |
| 8. 2 · AM = 2 · DN | 8. Combine like terms. |
| 9. AM = DN | 9. Division Property of Equality |
| 10. AM = MB and DN = NC (from step 6) and AM = DN (from step 9), therefore AM = MB = DN = NC | 10. Transitive Property of Equality |
| 11. AM ≅ MB ≅ DN ≅ NC | 11. If segments are = in length, then they are ≅. |