1-2: Points, Lines and Planes

Undefined Terms

Term Description Name Diagram

Point

Line

Plane

Indicates location

Has no size

One capital letter

A

Straight pathExtends in opposite directionsHas no thicknessInfinitely many points

Any two points:

AB�������������� �

BA�������������� �

or

One lowercase letter: l

lA

B

Has no thicknessInfinitely many lines

Flat surfaceExtends without end

One uppercase letter: PThree points not on same line:

ABC

PA

B C

• Collinear:• Two or more points that lie on the same line

• Coplanar:• Three or more points that lie on the same plane• Lines on the same plane are coplanar

• Space:• Set of all points in three dimensions.

Types of Points

CA

B D

A B C

a. What are two other ways name ?

b. What are two ways to name plane Q?

c. What are the names of three collinear points?

d. What are the names of four coplanar points?

BA�������������� �

line l or

Example 1:

m

Q

F

C

E D

B

A

AB�������������� �

plane AEC plane ADC

points A, E, D points A, F, B

points A, E, C points A, E, B

Complete Got It? #1 p.12 b. plane RVS c. N, Q, Ta. RQ�������������� �

Defined Terms

Term Description Name Diagram

Segment

Ray

Opposite Ray

Part of a line

Two endpoints and all points between

Part of a lineOne endpoint and all points on the line on one side of endpoint

Endpoint and any point on the ray:

AB��������������

Form a line

Two rays that share the same endpoint

Two endpoints:

AB BAor

A B

A BC

Shared endpoint and any other point on each ray:

CA��������������

CB��������������

C

B

A

Example 2:

a. What are the names of the segments in the figure?

b. What are the names of the rays in the figure?

c. Which of the rays in part(b) are opposite rays?

, , MN NP MP

M

P

N

, , , , ,MP NP MN PN NM PM������������������������������������������������������������������������������������

and NP NM����������������������������

Complete Got It? #2 p.13

Postulates (statements assumed to be true)

• Postulate 1-1• Through any two points there is exactly one line.

• Postulate 1-2• If two distinct lines intersect, then they intersect

in exactly one point.

• Postulate 1-3• If two distinct planes intersect, then they intersect

in exactly one line.

A B

A

BC

DG

Example 3:

HG

F

A

D C

B

E

a. What is the intersection of and ?

b. What is the intersection of plane ABCD and ?

c. What is the intersection of plane ABGH and plane DCHG?

AG CG

AGG

A

HG�������������� �

Complete Got It? #3 p.14 a. plane BFE b. Two planes intersect in one line, so you need two common points to name the common line.

Postulate

• Postulate 1-4• Through any three noncollinear points there is

exactly one plane.

CA

B D

Example 4: Each surface of the box represents part of a plane

HG

F

A

D C

B

E

a. Which plane contains points A, B and C?

b. Which plane contains points E, H and C?plane ABCD

plane EHCB

Complete Got It? #4 p.15 JM�������������� �

a. plane LMNP b.

Homework: P. 16-17, #’s 8-22, 40-45