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 -

Segment Addition Postulate

Postulate 4 -

Angle Addition Postulate

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