Proof: Distance Symmetry Example 4
Let's prove the following theorem:
(distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance CB)
Proof:
# | Claim | Reason |
---|---|---|
1 | distance BC = distance CB | distance BC = distance CB |
2 | (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance BC) | if distance BC = distance CB, then (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance BC) |
3 | (distance CB) ⋅ (distance BC) = (distance CB) ⋅ (distance CB) | if distance BC = distance CB, then (distance CB) ⋅ (distance BC) = (distance CB) ⋅ (distance CB) |
4 | (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance CB) | if (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance BC) and (distance CB) ⋅ (distance BC) = (distance CB) ⋅ (distance CB), then (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance CB) |
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