2-5 Postulates
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Transcript 2-5 Postulates
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. Gand 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