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Chapter 1: Introduction to Geometry

# The Basics

Geometry is the branch of mathematics that deals with points, lines, planes, and figures, and examines their properties, measurements, and mutual relations in space. Geometry figures exist in every part of our lives from a star in the night sky as a point to a wire inside a house as a line and to the tallest and strangest building as a complex three-dimensional polygon. So it is very important to know geometry because it is an essential part of our lives. A person who doesn't know geometry is like having no eyesight because he/she can't perceive the world, which is filled with geometry figures.

Geometry starts with a point. All the geometry figures are consisted of points. A point is a dot. It has no length and size. It is only a representation of a position. When you have a great deal of points in a row or a column, you get a line. A line is made of an infinite number of points. It is endless and widthless. It extends simultaneously into two directions. When you take out part of a line, you get a segment. A segment is a finite number of points in a row or a column with two endpoints. It has length and is usually measured with ruler. When you combine a great deal of segments, you get a plane. A plane has length and width but no thickness. When you pile up a great deal of planes, you get a polygon, which is a three-dimensional figure in space. A polygon has length, width, and height. All things existing in the world are polygons from a subatomic particle, which is too small to see to an aircraft carrier, which is a huge complex polygon.

Now you can identify a geometric figure. But what about constructing one? Fortunately we do the same thing as we recognizing one. We construct a geometric figure by points. When you want a point, you just draw a point. When you want a segment, you need to connect at least two collinear points. Extend the segment at the two end points to both directions, you get a line. When you want a plane, you need to connect at least three non-collinear points. Finally, when you want a polygon, you need to connect at least four non-polar points.

When two lines or segments intersect and they are also not on the top of each other, you get four angles. Angles are measured in degrees. If two angles add up to 180 degrees, then they are supplementary; if two angles add up to 90 degrees, then they are complementary. If one segment intersect another segment in latter's midpoint, then the first segment is called the bisector of the second segment.

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