Parallel lines are two lines that are always the same distance apart and never touch. In order for two lines to be parallel, they must be drawn in the same plane, a perfectly flat surface like a wall or sheet of paper.
Parallel lines are useful in understanding the relationships between paths of objects and sides of various shapes. For example, squares, rectangles, and parallelograms have sides across from each other that are parallel.
In formulas, parallel lines are indicated with a pair of vertical pipes between the line names, like this:
AB || CD
Each line has many parallels. Any line that has the same slope as the original will never intersect with it. Lines that would never cross, even if extended forever, are parallel.
A triangle has three corners, called vertices. The sides of a triangle (line segments) that come together at a vertex form two angles (four angles if you consider the sides of the triangle to be lines instead of line segments). Only one of these angles contains the third side of the triangle in its interior, and this angle is called an interior angle of the triangle. In the picture below, the angles∠ABC, ∠BCA and ∠CAB are the three interior angles of the triangle. An exterior angle is formed by extending one of the sides of the triangle; the angle between the extended side and the other side is the exterior angle. In the picture, angle ∠ACD is an exterior angle.