Chapter 2: Postulates and Theorems

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.