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Geometry Chapter 1

Point in Synthetic Geometry An exact location with zero-dimensions, and a point is found on the number line.
Point in Discrete Geometry A dot with 3-dimensions, has size and shape
Point in Plane-Coordinate An ordered pair with zero-dimensions, made of real numbers.
Point in Network Geometry A node with zero dimensions.
Line in Discrete Geometry Dots with spaces between. Lines have thickness (3-D)
Line in Synthetic Geometry Shortest, straight distance between two points. A line is dense, and infinitely extends in opposite directions. (Number line)
Line in Plane Coordinate Geometry Set of ordered pairs (x, y) that satisfy the equation Ax+By=C. Line is dense, straight, and continues on in opposite directions.
Line in Network Geometry A line segment or arc that connects one or two nodes together. There may be an infinite number of lines/arcs between two nodes.
Geometric Undefined Terms Cannot be defined by using other figures. Ex: Point, Line, and Plane.
Number Line Assumption Every line can be made to correspond to the real number, once zero and one are designated on the number line.
Parallel Lines Lines that lie in the same plane and have no point in common
Unique Line Assumption through any two points, there is exactly one line
Dimension Assumption #1) Given a line in a plane, there is at least one point in the plane, not on the line. #2) Given a plane in a space, there is one point in space not on that plane.
Pixel A tiny dot that creates an image on the computer monitor or screen.
One Dimensional Figures A figure in which all points are collinear (line segment, line, and ray).
Two Dimensional Figures A figure that's not collinear, but coplanar. Ex: Box, Triangle, Circle, etc.
Three Dimensional Figures Figures that are not coplanar; cannot be contained in the same plane. Ex: Football, backpack, humans, rectangular prism.
How can discrete lines intersect? At a point or a space.
Segment Consists of two endpoints, and all points between two endpoints.
Endpoints A place where a line segment (or ray) begins and ends.
Ray Part of a line with one endpoint that continues infinitely in one direction.
Opposite Rays Two rays that have the same endpoint and form a line.
Unique Distance Property Between any two points, there is a unique distance.
How do you find the distance between two points? Take the absolute value of the difference. Ex: |A-B| or |B-A|
Vanishing Points The point at the horizon line at which parallel lines appear to converge
Created by: aliciaobermann