1.2 Points, Lines, and Planes1.2 Points, Lines, and Planes

What is a definition?What is a definition?

Known words used to describe a new wordKnown words used to describe a new word

Undefined termsUndefined terms – are terms not formally – are terms not formally defined.defined.

There are three undefined terms in geometry: There are three undefined terms in geometry:

1. Point1. Point 2. Line2. Line 3. Plane3. Plane

PointPoint

1. A location in space.1. A location in space.

2. Has no dimension (no length, no width, 2. Has no dimension (no length, no width, no depth). no depth).

3. Usually represented by a dot.3. Usually represented by a dot.

4.4. Named using one capital letter.Named using one capital letter.

5.5. All geometric figures consist of points All geometric figures consist of points POINTS ARE TO GEOMETRIC FIGURES AS POINTS ARE TO GEOMETRIC FIGURES AS

___________ IS TO HUMANS?___________ IS TO HUMANS?

PointPoint

For example:For example:

●●BB

What would be a real world example of a point?

LineLine

1.1. A series of points that extends in opposite A series of points that extends in opposite directions without end. directions without end.

2.2. One-dimensional (length).One-dimensional (length).

3.3. Has an arrowhead on each end Has an arrowhead on each end representing the fact that it goes on representing the fact that it goes on forever. forever.

4.4. Always straight.Always straight.

5.5. Named with a lowercase script letter or by Named with a lowercase script letter or by 2 points on the line2 points on the line

LineLine

AA BB

ll

Can be called:Can be called:

Line Line ll

Line AB or ABLine AB or AB

Line BA or BALine BA or BA

For example:For example:

Real World example?

PlanePlane

1.1. A flat surface that extends forever in two A flat surface that extends forever in two dimensions (length & width).dimensions (length & width).

2.2. Contains infinitely many points and lines.Contains infinitely many points and lines.

3.3. Usually represented by a four-sided Usually represented by a four-sided figure.figure.

4.4. Named with a capital script letter or 3 Named with a capital script letter or 3 points on the surface of the planepoints on the surface of the plane

PlanePlane

AA

BC

W Can be named:Can be named:

Plane Plane WW

Plane ABC, plane BCA, plane Plane ABC, plane BCA, plane CBA, etc.CBA, etc.

**Planes can be named by more **Planes can be named by more than 3 points, but they must be than 3 points, but they must be named in either a clockwise or named in either a clockwise or counter-clockwise mannercounter-clockwise manner

For example:For example:

Real World example?

Horizontal Planes – Ceiling and Floor

Horizontal Planes – Two sides horizontal and no sides vertical

Vertical Planes – Walls Vertical Planes – two sides are vertical

More DefinitionsMore Definitions

CoCollinear points –llinear points –

points that points that cancan lie on the lie on the same line.same line.

**Think of the suffix “CO” as sharing.**

More DefinitionsMore Definitions

Noncollinear points –Noncollinear points –

D

More DefinitionsMore Definitions

Coplanar points – What does it mean?Coplanar points – What does it mean?

points that points that cancan lie on the same plane. lie on the same plane.

More DefinitionsMore Definitions

If the points do not lie in the same plane they If the points do not lie in the same plane they are?are?

Noncoplanar points – Noncoplanar points –

D

A

More DefinitionsMore Definitions

Equidistant – equally distantEquidistant – equally distant

Classify each statements as true or false

REMOTE TIME !

Question 1

PF ends at P

Question 2

Point S is on an infinite number of lines

Question 3

A plane has no thickness

More DefinitionsMore Definitions

IntersectIntersect – – – Two or more figures intersect if they have one or Two or more figures intersect if they have one or

more points in common.more points in common.– Think “meet” or “Cut”Think “meet” or “Cut”

IntersectionIntersection – – – All points or sets of points the figures have in All points or sets of points the figures have in

common.common.– Depending on what is intersecting, the Depending on what is intersecting, the

intersection will be differentintersection will be different

When a line and a point intersect, When a line and a point intersect, their intersection is a point.their intersection is a point.

BB

ll

Like taking a road trip and driving through a certain town

or city on the map.

When 2 lines intersect, their When 2 lines intersect, their intersection is a point.intersection is a point.

Like the intersection of Foothill and Ramsdale

When 2 planes intersect, their When 2 planes intersect, their intersection is a line.intersection is a line.

The planes are cutting

through one another

When a line and plane intersect, their When a line and plane intersect, their intersection is a point.intersection is a point.

Like sticking a pencil through a piece of paper

Questions???Questions???

Question 4

Collinear points are coplanar

Question 5

Planes have edges

Question 6

Two planes intersect in a line segment

Question 7

Two intersecting lines meet in exactly one point

Question 8

Points have no size

Question 9

Line XY can be denoted as XY or YX.

Partner Share: True or False

All points on a line are coplanar

True or False

A line has one endpoint

True or False

A point is named by a capital letter.

True or False

Two lines intersect in two points.