Download 1 Similarities and differences between regular and irregular polygons

1 Similarities and differences between regular and
irregular polygons (OUTLINE)
Wm E Todd-Brown 2010
2 Introduction
2.1
Thesis: Regular and irregular polygons share
basic properties of polygons but differ in the
congruency of their sides and interior angles.
3 Similarities
3.1
Both are polygons
3.1.1
Closed two-dimensional figure constructed a
finite number straight sides composed of line
segments that intersect exactly with two other noncollinear line segments, one at each of its endpoints
(vertices).
3.1.2
Specific polygon names are based on the
consecutive enumeration of vertices
3.1.3
General polygon class names are based on
the number of sides
3.2
Sides
3.2.1
Distance between each line segment vertices
can be measured.
3.2.2
Polygon perimeters are calculated from the
sum of the line segment measures
3.3
Interior Angles
3.3.1
Intersection of two adjacent line segments at
each vertex define the polygons interior angles
3.3.2
Angular measure for each interior angle can
be measured
3.3.3
Sum of the interior angle measures is a
constant for a particular class of polygons
4 Differences
4.1
Regular polygons
4.1.1
As demonstrated by the regular pentagon in
Figure 1 and the regular quadrilateral in Figure 2
4.2
4.1.1.1 All sides are congruent and all interior
angles are congruent
4.1.1.2 Are convex (all interior angles are less
than 180 degrees)
Irregular polygons
4.2.1
As demonstrated by the irregular pentagons
in Figure 1 and the irregular quadrilaterals in Figure 2
4.2.1.1 Either the sides are not congruent, or the
interior angles are not congruent, or both the sides
and the interior angles are not congruent
4.2.1.2 May be either convex or concave (one or
more interior angles greater than 180 degrees)
5 Conclusion
5.1
Both regular and irregular polygons adhere to
the basic definition of a polygon
5.2
Primary difference based on segment and angle
congruence
5.2.1
Regular polygons exhibit congruency for both
sides and interior angles
5.2.2
Irregular polygons exhibit some level of
incongruence in the sides or the interior angles, or
both
6 Figures
6.1
Figure 1
7.1
Figure 2
7
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