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.
