Proof: Midpoint Distance 2

Let's prove the following theorem:

if M is the midpoint of line AB, then (distance MB) ⋅ 2 = distance AB

Proof:

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Given

1	M is the midpoint of line AB

Proof Table

#	Claim	Reason
1	(distance AM) + (distance MB) = distance AB	if M is the midpoint of line AB, then (distance AM) + (distance MB) = distance AB (Midpoint Sum)
2	distance AM = distance MB	if M is the midpoint of line AB, then distance AM = distance MB (Midpoint Property)
3	(distance MB) + (distance MB) = distance AB	if (distance AM) + (distance MB) = distance AB and distance AM = distance MB, then (distance MB) + (distance MB) = distance AB (Substitution 8)
4	(distance MB) ⋅ 2 = distance AB	if (distance MB) + (distance MB) = distance AB, then (distance MB) ⋅ 2 = distance AB (double)

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