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

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

4. Named using one capital letter. 4. Named using one capital letter.

PointPoint

For example:For example:

●●BB

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:

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.

For example:For example:

More DefinitionsMore Definitions

Collinear points –Collinear points –

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

More DefinitionsMore Definitions

Noncollinear points –Noncollinear points –

D

More DefinitionsMore Definitions

Coplanar points – Coplanar points –

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

More DefinitionsMore Definitions

Noncoplanar points – Noncoplanar points –

D

A

More DefinitionsMore Definitions

Equidistant – equally distantEquidistant – equally distant

More DefinitionsMore Definitions

IntersectIntersect – –

Two or more figures intersect if they Two or more figures intersect if they have one or more points in common.have one or more points in common.

IntersectionIntersection – –

All points or sets of points the All points or sets of points the figures have in common.figures have in common.

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

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

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

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

Questions???Questions???

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

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.

Horizontal Planes – Ceiling and Floor

Horizontal Planes – Two sides horizontal and no sides vertical

Vertical Planes – Walls Vertical Planes – two sides are vertical

Group Practice

Vertical line l intersects a horizontal plane M at point O

l

MO

Group Practice

Horizontal plane Q and vertical plane N intersect

Group Practice

Point P is not in Plane N. Three lines through point P intersect N in points A, B, and C.

Remote Time !

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.

True or False

The edge of a plane is a line.