Proof: Divide Distances
Let's prove the following theorem:
(distance AB) / (distance CD) = (distance BA) / (distance DC)
Proof:
# | Claim | Reason |
---|---|---|
1 | distance AB = distance BA | distance AB = distance BA |
2 | distance CD = distance DC | distance CD = distance DC |
3 | (distance AB) / (distance CD) = (distance BA) / (distance CD) | if distance AB = distance BA, then (distance AB) / (distance CD) = (distance BA) / (distance CD) |
4 | (distance AB) / (distance CD) = (distance BA) / (distance DC) | if (distance AB) / (distance CD) = (distance BA) / (distance CD) and distance CD = distance DC, then (distance AB) / (distance CD) = (distance BA) / (distance DC) |
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