Basic Concepts Of Geometry

Geometry is one of the oldest branches of mathematics. Applications of geometric constructions were made many centuries ago, long before the mathematical principles on which the constructions were based were recorded. Geometry is a mathematical study of points, lines, planes, closed flat shapes, and solids. Using any one of these alone, or in combination with others, it is possible to describe, design, and construct every visible object. The purpose of this section is to provide a foundation and a clear understanding of geometric principles and a platform on which many practical problems depend for solution.


Terms

There are a number of terms used in geometry.

1. A plane is a flat surface.

2. Space is the set of all points.

3. Surface is the boundary of a solid.

4. Solid is a three-dimensional geometric figure.

5. Plane geometry is the geometry of planar figures (two dimensions).

Examples are: angles, circles, triangles, and parallelograms.

6. Solid geometry is the geometry of three-dimensional figures. Examples are: cubes, cylinders, and spheres.

Points

A point can be envisioned as an infinitely tiny sphere, having height, width, and depth all equal to zero, but nevertheless possessing a specific location.

Lines

A line is the path formed by a moving point. A length of a straight line is the shortest distance between two nonadjacent points and is made up of collinear points.

Line Segment

The portion of a line between two different points A and B is called a line segment. The points A and B are called the end points. A line segment can theoretically include both of the end points, only one of them, or neither of them.

Ray

A ray is an infinite set of collinear points extending from one end point to infinity.

Parallel

Two or more straight lines are parallel when they are coplanar (contained in the same plane) and do not intersect; that is, when they are an equal distance apart at every point.

Important Facts

The following facts are used frequently in plane geometry. These facts will help you solve problems in this section.

1. The shortest distance between two points is the length of the straight line segment joining them.

2. A straight line segment can be extended indefinitely in both directions.

3. Only one straight line segment can be drawn between two points.

4. A geometric figure can be moved in the plane without any effect on its size or shape.

5. Two straight lines in the same plane are either parallel or they intersect.

6. Two lines parallel to a third line are parallel to each other.