Technical Mathematics, Sixth Edition

6.2. Triangles

6.2.1. Polygons

A surface is a geometric figure consisting of those points that satisfy a particular condition. For example, a plane is a surface in which a straight line connecting any two of its points lies entirely in the surface. Figures lying entirely in a plane surface are called plane figures.

A polygon is a plane figure formed by three or more line segments, called the sides of the polygon, joined at their endpoints, as in Fig. 6-19. The set of all points inside the polygon is called its interior. The points where two sides meet is called a vertex. An interior angle is the angle at a vertex, measured from one side to the adjoining side, through the interior of the polygon.

Figure 6.19. A polygon.

The length of a side is given in units of length (inches, meters, etc.) and the area of an interior is given in square units (square inches, square meters, etc.).

If the sides of the polygon are equal and its interior angles are equal, it is called a regular polygon, Fig. 6-20.

Figure 6.20. Some regular polygons.

6.2.2. Triangles

A triangle is the simplest polygon, having three sides. The angles between the sides are the interior angles of the triangle, usually referred to as simply the angles of the triangle.

As shown in Fig. 6-21, a scalene triangle has no ...