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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