Proof: Midpoint Theorem

Let's prove the following theorem:

Proof:

Proof Table

#	Claim	Reason
1	distance XM = distance MY	if M is the midpoint of line XY, then distance XM = distance MY (Midpoint Property)
2	(distance XM) + (distance MY) = distance XY	if M is the midpoint of line XY, then (distance XM) + (distance MY) = distance XY (Midpoint Sum)
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 (Substitute 2)
4	(distance XM) + (distance XM) = (distance XM) ⋅ 2	(distance XM) + (distance XM) = (distance XM) ⋅ 2 (addition_theorem)
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 (Transitive Property of Equality Variation 2)
6	distance XM = (distance XY) ⋅ (1 / 2)	if (distance XM) ⋅ 2 = distance XY, then distance XM = (distance XY) ⋅ (1 / 2) (Multiply by 2)

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