Understanding Basic Geometry Terms: Points, Lines, and Planes
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
