2-5 Postulates
Ms. Andrejko
Real World
Vocabulary
 Postulate/Axiom- is a statement that is accepted as true
without proof
 Proof- a logical argument in which each statement that you
make is supported by a postulate or axiom
 Theorem- a statement that has been proven that can be used
to reason
 Deductive Argument- forming a logical chain of
statements linking the given to what you are trying to prove
Steps to a proof
 1. List the given information and if possible, draw a diagram
 2. State the theorem or conjecture to be proven.
 3. Create a deductive argument
 4. Justify each statement with a reason (definition, algebraic
properties, postulates, theorems)
 5. State what you have proven (conclusion)
Postulates
 2.1-2.7
 Midpoint theorem
Examples
 Explain how the figure illustrates that each statement is true.Then
state the postulate that can be used to show each statement is true.
1. The planes J and K intersect at line m.
Postulate: If 2 planes intersect, then their
intersection is a line.
2.
The lines l and m intersect at point Q.
Postulate: If 2 lines intersect, then their intersection
is exactly one point.
Practice
 Explain how the figure illustrates that each statement is true.Then
state the postulate that can be used to show each statement is true.
1.
Line p lies in plane N.
Postulate: If 2 points lie in a plane, then the
entire line containing those points lies in that
plane.
2.
Planes O and M intersect in line r.
Postulate: If 2 planes intersect, then their
intersection is a line.
Examples
 Determine whether each statement is always, sometimes, or
never true. Explain your reasoning.
1.
The intersection of two planes contains at least two points.
ALWAYS. The intersection of 2 planes is a line, and we must
have at least 2 points in order to create a line.
2.
If three planes have a point in common, then they have a
whole line in common.
SOMETIMES. 3 planes can intersect at the same line which
contains the same point, but they don’t have to.
Practice
 Determine whether each statement is always, sometimes, or
never true. Explain your reasoning.
1.
Three collinear points determine a plane
2.
Two points A and B determine a line
NEVER. Postulate tells us that we must have 3 noncollinear
points
ALWAYS.You can always create a line through any 2 points.
3.
A plane contains at least three lines
SOMETIMES. A plane may contain 3 lines, but it doesn’t have
to contain any lines in order to be a plane.
Examples
 In the figure, line m and
TQ lie
in plane A. State the postulate
that can be used to show that each statement is true.

1.
Points L, and T and line m lie in the same plane.
2.5: If 2 points lie in a plane, then the entire line
containing those points lies in that plane
1.
Line m and ST intersect at T.
2.6: If 2 lines intersect, then their
intersection is
 exactly one point
Practice
 In the figure, DG and DP are in plane J and pt. H lies on DG
State the postulate that can be used to show each statement is
true.
 collinear.

1. Gand H are
2.3: A line contains at least 2 points.
1.
Points D, H, and P are coplanar.
2.2: Through any 3 noncollinear points,
there is exactly one plane