Introduction to Postulates and Theorems

Introduction to basic postulates and theorems of points, lines, and planes.

1. 09/27/07
Warm-up
Which of the following
four statements can’t you
conclude from the
diagram?
B.A, B, and C are collinear.
C.B is the midpoint of AC.
D.DBC is a right angle.
E.E is in the interior of 
DBA
D
CBA
E

2. Postulate vs. Theorem
Postulate (axiom):
A statement that is accepted as true
without proof.
Theorem:
An important statement that must be
proved before it can be accepted.

3. Reading postulates and
theorems
Read carefully.
Reread each phrase, one at a time.
Look up any words you do not understand.
Try to identify conditions.
Look for key words, if, if and only if, exactly one,
exists, unique, etc.
Visualize, draw diagrams, or model the situation
Imagine if it wasn’t true. What would that look like?

4. Postulates
A line contains at least two
points;
space contains at
least four points not
all in one plane.
A plane contains at least three
points not all in one line;

5. More Postulates
Through any two points there is exactly one
line.

6. More Postulates
and through any
three noncollinear
points there is
exactly one plane.
Through any three
points there is at
least one plane,

7. More Postulates
If two points are in a plane, then the line that
contains the points is in that plane.

8. More Postulates
If two planes intersect, then their
intersection is a line.

9. p. 24: State a postulate, or part of a
postulate, that justifies your answer to each
exercise.
1.Name two points that
determine line l.
2.Name three points that
determine plane M.
3.Name the intersection
of planes M and N.
4.Does AD lie in plane
M?
5.Does plane N contain
any points not on AB?
M
N
B
A
l
C

10. Assignment A14
p. 25 #5-11

11. Theorems
If two lines intersect, then they intersect in
exactly one point.

12. Theorems
Through a line and a point not in the line
there is exactly one plane.

13. Theorems
If two lines intersect, then exactly one plane
contains the lines.