Parallel lines are two or more lines that never intersect. Examples of parallel lines are all around us, in the two sides of this page and in the shelves of a bookcase. When you see lines or structures that seem to run in the same direction, never cross one another, and are always the same distance apart, there’s a good chance that they are parallel. In algebra, we use something more precise than appearance to recognize and create parallel lines. We use equations.
An exterior angle of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to , where is the corresponding internal angle between two adjacent sides (Zwillinger 1995, p. 270).
Consider the angles formed between a side of a polygon and the extension of an adjacent side. Since there are two directions in which a side can be extended, there are two such angles at each vertex. However, since corresponding angles are opposite, they are also equal. Confusingly, a bisector of an angle is known as an exterior angle bisector, while a bisector of an angle (which is simply a line oriented in the opposite direction as the interior angle bisector) is not given any special name. The sum of the angles in a convex polygon is equal to radians (), since this corresponds to one complete rotation of the polygon.