Proof: Midpoint Theorem
Let's prove the following theorem:
if M is the midpoint of line XY, then distance XM = (distance XY) ⋅ (1 / 2)
Proof:
Given
1 | M is the midpoint of line XY |
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# | Claim | Reason |
---|---|---|
1 | distance XM = distance MY | if M is the midpoint of line XY, then distance XM = distance MY |
2 | (distance XM) + (distance MY) = distance XY | if M is the midpoint of line XY, then (distance XM) + (distance MY) = distance XY |
3 | (distance XM) + (distance XM) = distance XY | if (distance XM) + (distance MY) = distance XY and distance XM = distance MY, then (distance XM) + (distance XM) = distance XY |
4 | (distance XM) + (distance XM) = (distance XM) ⋅ 2 | (distance XM) + (distance XM) = (distance XM) ⋅ 2 |
5 | (distance XM) ⋅ 2 = distance XY | if (distance XM) + (distance XM) = (distance XM) ⋅ 2 and (distance XM) + (distance XM) = distance XY, then (distance XM) ⋅ 2 = distance XY |
6 | distance XM = (distance XY) ⋅ (1 / 2) | if (distance XM) ⋅ 2 = distance XY, then distance XM = (distance XY) ⋅ (1 / 2) |
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