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if a=b then b=a
symmetric property
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if a=b and b=c, then a=c
transitive property
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if a =b, then a+c = b+c
addition property of equality
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if a=b, then a-c= b-c
subtraction property of equality
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if a=b, then a times c= b times c
AxC = BxC
multiplication property of equality
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if a=b, then a/c=b/c
(c does not equal 0)
division property of equality
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if a=b, then you may replace b with a in any expression
substitution property of equality
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a(b+c)=ab+ac
distribution property
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Through any 2 points, there is exactly one line
postulate 2-1
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Through any 3 collinear points there is exactly 1 plane.
Postulate 2-2
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A line contains at least 2 points
Postulate 2-3
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A plane contains at least 3 points, not all on the same line
Postulate 2-4
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If 2 points lie on a plane then the entire line containing those 2 points lies in that plane
Postulate 2-5
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Two lines intersect in a line
Postulate 2-6
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Two planes intersect in a line
Postulate 2-7
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IF M is midpoint of segment AB, then segment AM is congruent to segment MB
Midpoint theorem
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The points on any line or line segment can be paired with real numbers so that, given any 2 points, A and B on a line, A corresponds to zero, and B corresponds to a positive real number
Ruler Postulate
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If A, B, and C are collinear and B is between A and C, then AB+BC= AC. If AB+BC=AC, then B is between A and C.
Segment Addition Postulate
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Congruence of segments is reflexive, symmetric, and transitive
theorem 2-2
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