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Obj. 4 Points, Lines, & PlanesObjectives

Identify and correctly label points, lines, line segments,rays, and planes.

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postulate

point

A statement that is accepted as true

without proof. Also called an axiom.

A location in space, represented by a

capital letter.

A Point A

Notation: A point is always labeled with acapital printed letter. It has no size one point is not bigger than another.

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line A straight path that has no thickness and

extends forever in both directions.

Example:

AB or line

Notation: A line is labeled either by twopoints or a single lowercase letter. Theorder of the two letters does not

matter. (AB is the same as BA.)

AAAA

BBBB

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collinear

noncollinear

Points that lie on the same line.

Example:

Points A, B, and C are collinear.

Points that do not lie on the same line.

Points A, B, and D are noncollinear

Note: Two points are always collinear.

A

C

B

D

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Examples

1. Are points G, H, and J collinear ornoncollinear?

2. Are points F, H, and K collinear ornoncollinear?

3. Are points J and K collinear or

noncollinear?

F

H

G

J

K

collinear

noncollinear

collinear

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line segment

ray

Part of a line consisting of two points,

called endpointsendpointsendpointsendpoints, and all points betweenthem.

Part of a line that starts at an endpointand extends forever in one direction.

Notation: The order of the letters doesmatter for the name of a ray.

AAAABBBB

AB or BA

AAAA

BBBB

AB

AB is not the same as BA

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opposite rays Two rays that have a common endpoint and

form a line.

QQQQ RRRR

SSSS

RS and RQ are opposite rays

Note: You could also write RQ as QR.

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plane A flat surface that has no thickness and

extends forever.

Plane ABC or planeR

Notation: A plane is named either by ascript capital letter or three

noncollinear points.

A

B

C

R

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coplanar

noncoplanar

Points that lie in the same plane.

Example:

Points A, B, C, and D are coplanar.

Points that do not lie in the same plane.

Points A, B, C, and E are noncoplanar.

Note: Three noncollinear points are alwayscoplanar.

A

B

C

R

E

D

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Example Find three different ways you can name the

plane below.

Plane Tor any three letters except S

S

F R

D

ET

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Post. 1-1-1: Through any two points there is

exactly one line.

Post. 1-1-2: Through any three noncollinearpoints there is exactly one planecontaining them.

Post. 1-1-4: If two lines intersect, then they

intersect in exactly one point.

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Post. 1-1-5: If two planes intersect, then

they intersect in exactly one line.

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Examples:

1. The intersection ofplanes Hand E is____ or ____.

2. The intersection ofmand n is ____.

3. Line kintersects Eat ____.

4. R, X, and S are

__________.

n

XXXX

YYYY

collinearcollinearcollinearcollinear

k

E

H

m

n

R

X

S

Y

RSRSRSRS