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