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Geometry Chapter 1
Term | Definition |
---|---|
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 |