When points, lines, and planes are put together, they form more complex geometric shapes. In basically every geometric figure that we'll study, angles are formed between lines, segments or rays. In this section, we'll study angles and their special properties. Not only are there many different ways to classify angles, but each classification has many consequences. The properties of angles also determine the relationship between rays, lines, and components of figures. Based on the angles formed when lines intersect, those lines can be classified as parallel, perpendicular, or something in between. These two properties of angles, parallelism and perpendicularity, are probably the most important concepts of plane geometry. Although they are only two very special kinds of angles, and would only occur rarely if angles were formed at random, they are still important.
In the real world, angles are not formed at random. When you consider the roads, buildings, and everyday objects that make up the world, you notice that the world is constructed chiefly with parallel and perpendicular lines. In addition to understanding the significance of angle properties, we'll see how to divide angles and segments, and how this can help us down the road.