Proof: Midpoint Distance 2
Let's prove the following theorem:
if M is the midpoint of line AB, then (distance MB) ⋅ 2 = distance AB
Proof:
Given
| 1 | M is the midpoint of line AB |
|---|
| # | Claim | Reason |
|---|---|---|
| 1 | (distance AM) + (distance MB) = distance AB | if M is the midpoint of line AB, then (distance AM) + (distance MB) = distance AB |
| 2 | distance AM = distance MB | if M is the midpoint of line AB, then distance AM = distance MB |
| 3 | (distance MB) + (distance MB) = distance AB | if (distance AM) + (distance MB) = distance AB and distance AM = distance MB, then (distance MB) + (distance MB) = distance AB |
| 4 | (distance MB) ⋅ 2 = distance AB | if (distance MB) + (distance MB) = distance AB, then (distance MB) ⋅ 2 = distance AB |
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