Shape 

Copyright David & Cynthia Thomas, 2009

 

Naming, Describing, and Constructing Polygons--Directed Activity: Names & Attributes of N-gons

 

Chapter Three focuses on the properties of quadrilaterals, regular polygons, and circles.  The following six questions provide a conceptual context in which to consider those properties:

1.      What are the characteristic features of quadrilaterals?  Of regular polygons? Of circles?

2.      What hierarchical relationships exist between quadrilaterals with different side and angle characteristics?

3.      Using The Geometers Sketchpad and paper folding, how do you construct a square?  A parallelogram?

4.      What information is needed to determine the perimeter of a polygon?  The circumference of a circle? 

5.      What information is needed to determine the area of a lattice  quadrilateral?  A regular polygon?  A circle?

6.      What is the relationship between area and perimeter in quadrilaterals?  In regular polygons? 

                                 

Focus

Polygon angle sums

Background

Figure 3.1 illustrates several types of polygon angles:

·        Interior angles are formed by the sides of the polygon (e.g., ÐABC)

·        Exterior angles are formed by extending one side of the polygon at a vertex (e.g., ÐXBC)

·        Central angles such as ÐAPB are associated with regular polygons.

Figure 3.1: Polygon Angles

Tasks

Using the shading as a hint, determine the sum of the

·        Interior angles for each polygon

·        Exterior angles for each polygon