Proof: Distance Symmetry Example 4

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	distance BC = distance CB	distance BC = distance CB (Distance Equality Property)
2	(distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance BC)	if distance BC = distance CB, then (distance BC) ⋅ (distance BC) = (distance CB) ⋅ (distance BC) (Multiplicative Property of Equality)
3	(distance CB) ⋅ (distance BC) = (distance CB) ⋅ (distance CB)	if distance BC = distance CB, then (distance CB) ⋅ (distance BC) = (distance CB) ⋅ (distance CB) (Multiplicative Property of Equality Variation 1)
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) (Transitive Property of Equality)

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