Given AB =28; M lies on the line AB

Question

Prove: M is a midpoint.
Between A and M is the equation 2x+2, between M and B is the equation 4x=10
match the correct statements with the correct reasons

Statements: Reasons:
1. M lies on AB, AB= 28 1. ?
2. AM+MB=AB 2.?
3. 2x+2+4x-10=28 3. Substitution property
4. 6x-8=28 4?
5. 6x=36 5. ?
6. x=6 6?
7. AM = 2(6)+2 and MB=4(6)-10 7. Substitution property
8. AM=14 and MB - 14 8. Simplifying
9. M is a midpoint 9. ?

Word bank:
Addition Property of equality
combine like terms
definition of a midpoint
division property of equality
given
segment addition postulate
simplifying
substitution property
substitution property

Answer 1

Here are the appropriate reasons matched with each statement:

1. M lies on AB, AB = 28.
   Reason: 1. Given

2. AM + MB = AB.
   Reason: 2. Segment addition postulate

3. 2x + 2 + 4x - 10 = 28.
   Reason: 3. Substitution property

4. 6x - 8 = 28.
   Reason: 4. Combine like terms

5. 6x = 36.
   Reason: 5. Addition property of equality

6. x = 6.
   Reason: 6. Division property of equality

7. AM = 2(6) + 2 and MB = 4(6) - 10.
   Reason: 7. Substitution property

8. AM = 14 and MB = 14.
   Reason: 8. Simplifying

9. M is a midpoint.
   Reason: 9. Definition of a midpoint

In summary, the correct reasons for each statement have been provided from the word bank, illustrating a logical progression to conclude that point M is indeed the midpoint of segment AB.