SOLUTION: Complete the formal proof of the theorem.
If two line segments are congruent, then their midpoints separate these segments into four congruent segments.
Line segment A B is abo
Algebra ->
Angles
-> SOLUTION: Complete the formal proof of the theorem.
If two line segments are congruent, then their midpoints separate these segments into four congruent segments.
Line segment A B is abo
Log On
Question 1191305: Complete the formal proof of the theorem.
If two line segments are congruent, then their midpoints separate these segments into four congruent segments.
Line segment A B is above line segment D C. The two segments appear to be the same length. Points M and N are the midpoints of segments A B and D C, respectively.
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
Correct: Your answer is correct.
2.
AB = DC
Correct: Your answer is correct.
2. If segments are ≅, then they are = in length.
3. AB = AM + MB;
AM + MB = DN + NC
Incorrect: Your answer is incorrect.
3.
Given
Incorrect: Your answer is incorrect.
4.
AM = MB = DN = NC
Incorrect: Your answer is incorrect.
4. Substitution
5.
M is the midpoint of AB;
N is the midpoint of DC.
5.
Given
Correct: Your answer is correct.
6.
AM = MB and DN = NC
Correct: Your answer is correct.
6. The midpoint of a segment forms two segments = in measure.
7. AM + AM = DN + DN 7.
Substitution
Correct: Your answer is correct.
8.
2 · AM = 2 · DN
8. Combine like terms.
9. AM = DN 9.
Division Property of Equality
Correct: Your answer is correct.
10.
AM + MB = DN + NC
Incorrect: Your answer is incorrect.
10. Substitution
11.
AM ≅ MB ≅ DN ≅ NC
11.
If segments are = in length, then they are ≅.
You can put this solution on YOUR website! 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 ≅. |
