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