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
2.
3.
4.
5.
1.
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:
A
B l
Can be called:
Line l
Line AB or AB
Line BA or BA

Plane
2.
3.
1.
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:
A W
C
B
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.

Classify each statements as true or false

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

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.