Proof: Equal Length Segments

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	(distance XY) + (distance YZ) = distance XZ	if m∠XYZ = 180, then (distance XY) + (distance YZ) = distance XZ (Length is Sum of Parts)
2	distance WY = (distance WX) + (distance XY)	if m∠WXY = 180, then distance WY = (distance WX) + (distance XY) (Collinear Points Property)
3	distance WY = (distance YZ) + (distance XY)	if distance WY = (distance WX) + (distance XY) and distance WX = distance YZ, then distance WY = (distance YZ) + (distance XY) (Term 1 Substitution)
4	distance WY = (distance XY) + (distance YZ)	if distance WY = (distance YZ) + (distance XY), then distance WY = (distance XY) + (distance YZ) (Commutative Property Variation 1)
5	distance WY = distance XZ	if distance WY = (distance XY) + (distance YZ) and (distance XY) + (distance YZ) = distance XZ, then distance WY = distance XZ (Transitive Property of Equality)

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