1. Given: AB = 64; M lies on the line AB
AM = 4x + 4 BM= 6x-10
Prove: M is a midpoint.

Statements: Reason:
1) M lies on AB
AB= 64

2) AM + MB = AB -

3) 4x+4+6x-10=64 - Substitution Property

4) 10x- 6 = 64 -

5) 10x=70 -

6) x = 7 -

7) AM= 4(7) + 4 and
MB = 6(7) - 10 - Substitution Property

8) AM = 32 and MB = 32 - Simplifying

9) M is a midpoint.

Reasoning bank for #1

Addition Property of equality
Combine like terms
Definition of midpoint.
Division property of equality
Segment addition postulate