Basic Geometry Terms: Points, Lines, and Planes
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1-2: Points, Lines, and
Planes
Basic Geometry Terms
Undefined Terms
Definition of words
Consist of other words
How do you define the first word?
Philosophy Class?
Every end has a start
Every effect has a cause
Geometry undefined terms
Point, line, and plane
Used to build the definitions of other figures
Undefined Terms
Point – indicates a location and has no size
Line – represented by a straight path that
extends in two opposite directions without end
and has no thickness. A line contains infinitely
many points.
Plane – represented by a flat surface that
extends without end and has no thickness. A
plane contains infinitely many lines.
Undefined Terms
Collinear Points – points that lie on the same line
Coplanar – when points and/or lines lie on the same plane
Defined Terms
Segment – part of a line that consists of two endpoints and all points between
them.
Ray – part of a line that consists of one endpoint and all the points of the line
on one side of the endpoint
Opposite rays – two rays that share the same endpoint and form a line
Example
Use the diagram to answer each question.
-
Name two coplanar lines.
-
Name three non-collinear points.
-
Name the plane two different ways.
-
Name a pair of opposite rays.
Take Home Message
Undefined terms are used as building blocks of Geometry (and Math)
Geometry will have a lot of vocabulary words
The concepts will give us algebraic equations
Geometry will enhance our artistic abilities
1.2 Continued
Postulate – accepted statement of fact
Like undefined terms, used as building blocks of the logical system in geometry
Also known as axioms
Postulate 1.1
- through any two points, there is exactly one line
Postulate 1.2-
if two distinct lines intersect, then they intersect in exactly
one point.
1.2 Continued
Postulate 1.3-
if two distinct planes intersect, then they intersect in exactly
one line
1.2 Continued
Postulate 1.4 –
through any three noncollinear points, there is exactly one
plane
Where does Plane ABCD intersect
Plane ACEG?
What plane contains the points
C, D, and B?
What plane contains the points
E, F, and C?
Example
Take Home Message
Postulates are assumed to be true
No formal proof
Relationship between dimensions
A point is the intersection of two lines
A line is the intersection of two planes
A plane is the intersection of 3D figures
Discover the fundamental concepts in geometry such as points, lines, and planes, which serve as the foundation for defining other geometric figures. Explore the definitions of these terms, their properties, and how they are used to construct various shapes. Dive into the importance of undefined terms, defined terms, and key postulates in geometric reasoning.
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Presentation Transcript
1-2: Points, Lines, and Planes Basic Geometry Terms
Undefined Terms Definition of words Consist of other words How do you define the first word? Philosophy Class? Every end has a start Every effect has a cause Geometry undefined terms Point, line, and plane Used to build the definitions of other figures
Undefined Terms Point indicates a location and has no size Line represented by a straight path that extends in two opposite directions without end and has no thickness. A line contains infinitely many points. Plane represented by a flat surface that extends without end and has no thickness. A plane contains infinitely many lines.
Undefined Terms Collinear Points points that lie on the same line Coplanar when points and/or lines lie on the same plane
Defined Terms Segment part of a line that consists of two endpoints and all points between them. Ray part of a line that consists of one endpoint and all the points of the line on one side of the endpoint Opposite rays two rays that share the same endpoint and form a line
Example Y Use the diagram to answer each question. Name two coplanar lines. - Z Name three non-collinear points. V - X W Name the plane two different ways. - Name a pair of opposite rays. -
Take Home Message Undefined terms are used as building blocks of Geometry (and Math) Geometry will have a lot of vocabulary words The concepts will give us algebraic equations Geometry will enhance our artistic abilities
1.2 Continued Postulate accepted statement of fact Like undefined terms, used as building blocks of the logical system in geometry Also known as axioms Postulate 1.1- through any two points, there is exactly one line Postulate 1.2- if two distinct lines intersect, then they intersect in exactly one point.
1.2 Continued Postulate 1.3- if two distinct planes intersect, then they intersect in exactly one line
1.2 Continued Postulate 1.4 through any three noncollinear points, there is exactly one plane
Example A B Where does Plane ABCD intersect D Plane ACEG? C F What plane contains the points E C, D, and B? G H What plane contains the points E, F, and C?
Take Home Message Postulates are assumed to be true No formal proof Relationship between dimensions A point is the intersection of two lines A line is the intersection of two planes A plane is the intersection of 3D figures
