Statements
If p, then q
Conditional
Through any two points, there exists exactly one line
Two Point Postulate
a=a
Reflexive
All right angles are congruent
Right Angles Congruence Theorem
length of AB+length of BC= length of AC
Segment Addition Postulate
If not p, then not q
Inverse
If two points lie in a plane, then the line containing them lies in the plane
Plane-Line Postulate
If a=b and b=c, then a=c
Transitive
Vertical angles are congruent
Vertical Angles Congruence Theorem
Measure of angle ABC + Measure of angle CBD = Measure of angle ABD
Angle Addition Postulate
If not q, then not p
Contrapositive
If two lines intersect, then their intersection is exactly one point
Line Intersection Postulate
If a=b, then b=a
Symmetric
If two angles are supplementary to the same angle (or to congruent angles), then they are congruent.
Congruent Supplements Theorem
If a=b, then a+c=b+c
Addition Property of Equality
If q, then p
Converse
Through any three noncollinear points, there exists exactly one plane
Three Point Postulate
If a=b, then a can be substituted for b (or b for a) in any equation or expression
Substitution
If two angles are complementary to the same angle (or to congruent angles), then they are congruent.
Congruent Complements Theorem
If a=b, then ac=bc
Multiplication Property of Equality
p if and only if q
Biconditional
A line contains at least two points
Line-Point Postulate
5(x+8)=5x+40
Distributive Property
If two angles form a linear pair, then they are supplementary.
Linear Pair Postulate
If a=b, then a/c=b/c and c cannot equal 0
Division Property of Equality