Today we focused on explaining the undefined terms (point, line, plane, and space) and then building definitions for some simple geometric objects (segment, ray, angle, triangle).
For definitions to be universally understood, we need a set of terms that everyone understands and accepts without question. These are referred to "undefined terms." In geometry, the undefined terms are point, line, plane, and space.
A point is a zero-dimensional figure (i.e., it has no length, no width, and no height).
It is represented with a dot and labeled with a capital letter.
A line is a set of points extending infinitely in both directions and is one-dimensional (i.e., it has length, but no width or height).
It is represented by a (straight) line with arrowheads on both ends.
The notation we use to name lines is either two letters of points on the line with a double-headed arrow over them or a single, lower-case, script letter.
A plane is a two-dimensional (i.e., it has length and width, but no height) surface extending in all directions infinitely.
A plane is typically represented by a parallelogram (a vertical plane has a pair of vertical sides and a horizontal plane has a pair of horizontal sides) and is labeled as "plane XYZ," where X, Y, and Z are three points on the plane. Your textbook also uses the convention of naming planes with a single lower-case letter in one of the corners of the plane.
This video gives a brief description and demonstration of what I just summarized.
http://www.youtube.com/watch?v=GK3h7LzqsUg
Correction to video-
When naming planes: You should only use three letters when using points.
(We'll talk more about drawing three-dimensional figures later.)
The other topic we addressed in class was set theory. We focused primarily on the union (inclusive or) and intersect (and).
The union of two geometric objects is the set of points that are in either (or both) of the objects.
The intersection of two geometric objects is the set of points that are in both of the objects.
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