Geometry features many "special lines", that have different postulates and theorems about them. Some of these are; parallel lines, skew lines, parallel planes, transversals, corresponding angles, and alternate exterior angles. These all have things in common, and have differ as well.
When looking at the given geometric figures, one can easily group these into two groups. The first group being parallel lines, transversals, corresponding angles, and alternate exterior angles. The other group would then be parallel planes and skew lines.
Parallel lines are two lines that have domains, or ranges of (-infinity,infinity), meaning that these lines will continue onwards forever without ever crossing. When a line is drawn through these lines, it is called a transversal. With a transversal comes many different theorems and postulates. The alternate exterior angle theorem states that when a transversal goes through parallel lines, the outside angles will be congruent. Another theorem that comes with transversals in the corresponding angle theorem, which states the angles in corresponding corners of the transversal will be congruent.
Parallel planes are similar to parallel lines in which they will never cross, and continue to infinitiy. When you combine these parallel planes into a figure such as a cube you can have a special line called a skew line. A skew line is a line that in respect to a given plane does not have any relationship with the plane. Ex: Not parallel.
Oct 18th, 2014
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