Transcript 1.2 Points, Lines, & Planes

1.2 Points, Lines, and Planes
What is a definition?

Known words used to describe a new word
Undefined terms – are terms not formally
defined.
There are three undefined terms in geometry:
1. Point
2. Line
3. Plane
Point
1. A location in space.
2. Has no dimension (no length, no width, no
depth).
3. Usually represented by a dot.
4. Named using one capital letter.
Point
For example:
●B
Line
1.
2.
3.
4.
5.
A series of points that extends in opposite
directions without end.
One-dimensional (length).
Has an arrowhead on each end
representing the fact that it goes on
forever.
Always straight.
Named with a lowercase script letter or by
2 points on the line
Line
For example:
Can be called:
l
A
B
Line l
Line AB or AB
Line BA or BA
Plane
1.
2.
3.
4.
A flat surface that extends forever in two
dimensions (length & width).
Contains infinitely many points and lines.
Usually represented by a four-sided
figure.
Named with a capital script letter or 3
points on the surface of the plane
Plane
For example:
W
A
B
C
Can be named:
Plane W
Plane ABC, plane BCA, plane
CBA, etc.
More Definitions

Collinear points –
points that can lie on the same
line.
More Definitions

Noncollinear points –
D
More Definitions

Coplanar points –
points that can lie on the same plane.
More Definitions

Noncoplanar points –
A
D
More Definitions

Equidistant – equally distant
More Definitions


Intersect –
Two or more figures intersect if they
have one or more points in common.
Intersection –
All points or sets of points the
figures have in common.
When a line and a point intersect,
their intersection is a point.
l
B
When 2 lines intersect, their
intersection is a point.
When 2 planes intersect, their
intersection is a line.
When a line and plane intersect, their
intersection is a point.
Questions???
REMOTE TIME !
Classify each statements as true or
false
Question 1

PF ends at P
Question 2
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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
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Two intersecting lines meet in exactly one point
Question 8

Points have no size
Question 9
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Line XY can be denoted as XY or YX.
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Horizontal Planes – Ceiling and Floor

Horizontal Planes – Two sides horizontal and
no sides vertical
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Vertical Planes – Walls
Vertical Planes – two sides are vertical
l
Group Practice
Vertical line l intersects a horizontal plane M at point O
M
O
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.