Chapter 2: Postulates and Theorems
Through any two points there exists exactly one line.
A line contains at least two points.
If two lines intersect, then their intersection is exactly one point.
Through any three noncollinear points there exists exac
tly one plane.
A plane contains at least three noncollinear points.
If two planes intersect, then their intersection is a line.
If two points lie in a plane, then the line containing them lies in the
plane.
Law of Detachment: If p
q is a true statem
ent and p is true, then q is
true.
Law of Syllogism: If p
q and q
r, then p
r.
Statement:
If
H
, then
C
.
p
q
Inverse:
If not
H
, then not
C
.
~p
~q
Converse:
If
C
, then
H
.
q
p
Contrapositive:
If not
C
, then not
H
.
~q
~p
Right Angl
es Theorem:
All right angles are congruent.
Linear Pair Postulate:
If two angles form a linear pair, then they are
supplementary.
Vertical Angles Theorem:
Vertical angles are congruent.
The Congruent Complements Theorem: If two angles are
complement
ary to the same angle (or to congruent angles), then the
two angles are congruent.
The Congruent Supplements Theorem: If two angles are
supplementary to the same angle (or to congruent angles), then the
two angles are congruent.
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