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# Use Postulates and Diagrams

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by

## Juan Jorrin

on 5 December 2018

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#### Transcript of Use Postulates and Diagrams

Postulate 5
Postulate 1 -
Ruler Postulate
Postulate 3 -
Protractor Postulate
Identify a postulate illustrated by a diagram.
Postulate 8
1.
Use given information to sketch a diagram.
3. Sketch a diagram showing
AB CD
.
Postulate 10
Two points are lying in a plane. Then, the line containing them also lies in that plane.
Use Postulates and Diagrams
Postulate 2 -
Postulate 4 -
Postulate 6
Postulate 9
Postulate 11
Postulates and Theorems
A
postulate
is a statement that is assumed true without proof. It is also called an
axiom
.
A
theorem
is a true statement that has a proof.
Review:
A
B
x
x
1
2
On a number line, every point has a corresponding number and every number has a corresponding point.
Points
Coordinates
AB = |x - x |
2
1
A
C
B
AB
BC
AC
Given that point B lies between point A and point C, then
AC = AB + BC
A
B
C
D
Given that
D
is inside
ABC
and a ray is drawn from
B
to
D
, then
m
ABC
=
m
ABD
+
m
DBC
There exist an exactly one line passing through 2 points.
There is at least 2 points lying on the same line.
Postulate 7
There exist an exactly one point in the intersection of two lines.
There exist an exactly one plane through any 3 noncollinear points.
There is at least 3 points lying on the same plane.
The intersection of two planes is a line.
If
then
2.
If
then
Postulate 5

If there are two points, then there is exactly one line passing through these points.
Postulate 8

If there are three noncollinear points, then there is exactly one plane containing those points.
STEP 1
Draw CD.
C
D
STEP 2
Draw another line intersecting CD.
Make sure that the angle formed by the intersection is 90°.
Label the line AB.
A
B
STEP 3
STEP 4
Point
A
is on one side of
OB
. The ray
OA
has a corresponding real number from 0 to 180.
O
A
B
Full transcript