This chapter covers the basic language and terminology of plane geometry.

EO 1.1

IDENTIFY a given angle as either:

a. Straight

b. Acute

c. Right

d. Obtuse

EO 1.2

STATE the definitions of complimentary and supplementary angles.

Geometry is one of the oldest branches of mathematics. Applications of geometric constructions were made centuries 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 of geometric principles and constructions 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). are: angles, circles, triangles, and parallelograms.

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

Examples

are:

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. A line segment is a portion of a line. A ray is an infinite set of collinear points extending from one end point to infinity. A set of points is noncollinear if the points are not contained in a line.

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.

Angles

An angle is the union of two nonparallel rays originating from the same point; this point is known as the vertex. The rays are known as sides of the angle, as shown in Figure 1.

Figure 1 Angle

If ray AB is on top of ray BC, then the angle ABC is a zero angle. One complete revolution of a ray gives an angle of 360.

Figure 2 - 360 Angle

Depending on the rotation of a ray, an angle can be classified as right, straight, acute, obtuse, or reflex. These angles are defined as follows:

Right Angle - angle with a ray separated by 90.

Figure 3 Right Angle

Straight Angle - angle with a ray separated by 180 to form a straight line.

Figure 4 Straight Angle

Acute Angle - angle with a ray separated by less than 90.

Figure 5 Acute Angle

Obtuse Angle - angle with a ray rotated greater than 90 but less than 180.

Figure 6 Obtuse Angle

Reflex Angle - angle with a ray rotated greater than 180.

Figure 7 Reflex Angle

If angles are next to each other, they are called adjacent angles. If the sum of two angles equals 90, they are called complimentary angles. For example, 27 and 63 are complimentary angles. If the sum of two angles equals 180, they are called supplementary angles. For example, 73 and 107 are supplementary angles.

Summary

The important information in this chapter is summarized below.

Lines and Angles Summary

Straight lines are parallel when they are in the same plane and do not intersect.

A straight angle is 180.

An acute angle is less than 90.

A right angle is 90.

An obtuse angle is greater than 90 but less than 180.

If the sum of two angles equals 90, they are complimentary angles.

If the sum of two angles equals 180, they are supplementary angles.