Final answer:
The matches between the given statements and reasons are: ZM = MB and AZ = ZB.
Step-by-step explanation:
The given statements are:
ZA = 2B
M is the midpoint of AB
We need to match the reasons with the statements. Let's go through each given reason one by one:
A) ZM = MB
Reason: M is the midpoint of AB, so ZM and MB will be equal.
This matches with the given statement ZA = 2B, as ZA is twice the length of ZM and B is twice the length of MB.
B) AZ = ZB
Reason: M is the midpoint of AB, so AZ and ZB will be equal.
This matches with the given statement ZA = 2B, as AZ is equal to ZB and ZA is twice the length of ZB.
C) ZM = AB
Reason: This reason is not correct.
AB is the length of the whole segment, not just the midpoint.
D) ZA = AM
Reason: This reason is not correct.
ZA is twice the length of ZM, not equal to AM.
Therefore, the correct matches are:
A) Reason: M is the midpoint of AB
Matches with: ZM = MB
B) Reason: M is the midpoint of AB
Matches with: AZ = ZB