CHAPTER 2

POLYGONS

Most of the basic shapes, such as triangle, square, rectangle, are parts of a larger subset of closed figures bounded by broken lines called polygons.

The term “polygon” is a combination of two Greek words, “poly” which means “many” and “gonia” which means “angle”.

POLYGON- is a two-dimensional closed figure bounded

by straight line segments.

POLYGONS

1. Side or edge- is one side of the line segments that make up the polygon.

2. Vertex- is a point where the sides meet.

3. Diagonal- is a line connecting two non-adjacent vertices.

Parts of a Polygon

4. Interior angle- is the angle formed by two adjacent sides inside

the polygon.

5. Exterior angle- is the angle formed by two adjacent sides outside

the polygon.

6. Apothem (of a regular polygon)- is the segment connecting the center of a polygon

and the midpoint of a side. The apothem is also a perpendicular bisector of the side.

7. Central angle (of a regular polygon)- is the angle subtended by a side about the center.

apothem

diagonalside

Interiorangle Exteri

orangle

vertexCentralangle

a.

b.

c.

Figure 2.2

Typical polygons are illustrated in Figure 2.2-a.

Although figure 2.2-b is bounded by straight lines, it is not a polygon since it is not a closed figure.

The closed Figures in 2.2-c are non polygons since they are enclosed by curves.

Three major conditions are needed to classify a polygon.

◦First, it must be a two-dimensional figure.◦ Second, a polygon must be a closed figure.◦Lastly, it should be bounded by straight lines

Polygons are said to be similar if their corresponding interior angles are equal and their corresponding sides are proportional.

By ratio and proportion, we obtain the following equations from two similar polygons.

a)

where x1 and x2 are any two sides of a polygon and y1 and y2 are the corresponding sides of a similar polygon.

b) 2

where A1 and A2 are the areas of the two similar polygons with x and y as their corresponding sides respectively.

RADIN Types of polygons.pptx

FORMULAS molate.pptx