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Geometry

Geometry . Points, Lines, Planes. Undefined Terms. Point- a location in space; No set size/immeasurable no dimension; represented by a dot and a capital letter Line- contains at least two points; extends in opposite direction without end; No thickness/immeasurable one dimension

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Geometry

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  1. Geometry Points, Lines, Planes

  2. Undefined Terms • Point- • a location in space; • No set size/immeasurable • no dimension; • represented by a dot and a capital letter • Line- • contains at least two points; • extends in opposite direction without end; • No thickness/immeasurable • one dimension • represented by two points with line symbol above or italicized lowercase letter AB s • Plane • Contains at least 3 non-collinear points; • No thickness; goes in both directions without end/immeasurable • often represented by a four sided figure; • has two dimensions. • Names using a capital letter in the corner of the figure or by using three non-collinear points. • Why Undefined?Since a point, line and plane have no definite shape or size, they are considered “undefined”.

  3. Collinear points • Non-collinear points • Coplanar points • Non-coplanar points • Coplanar lines

  4. Postulatesstatements accepted without further justification • Through any two points there is exactly one line • Through any three non-collinear points there exists exactly one plane.

  5. Naming Points, Lines, Planes • Points are named with a capital letter • Lines are named by using two capital letters or an italicized lowercase letter • Planes are named with one capital letter

  6. More Definitions • Segment: a part of line with a definite starting and ending point. These points are called endpoints. • Ray: a part of a line with a definite starting point extending in one direction without end. • Opposite Rays: Two rays starting or sharing the endpoint and extending in opposite directions without end.

  7. Naming Segments and Rays • When naming a segment use the two endpoints with a line segment symbol above two capital letters denoting the endpoints. The order of the endpoints does not matter. • When naming a ray, you state the endpoint FIRST and then use any other point on the ray.

  8. Questions • How many points are on a line segment? • How many points are on a line? • Which segment is longer? • Which segment has more points? • How many points are on a ray? • Can you measure a ray?

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