The document discusses different types of polygons. It defines a polygon as a closed shape with three or more sides and distinguishes between convex polygons, where any two interior points can be connected by a line segment staying inside the figure, and concave polygons, where the line segment may pass outside. It also distinguishes between regular polygons with equal sides and angles and irregular polygons. Finally, it classifies polygons based on the number of sides they have, such as triangles having three sides, quadrilateral four sides, and so on.

1. POLYGONS
Understanding the properties of various shapes,
or figures, is going to be key throughout
Geometry.
In this lesson, we will explore some of these
shapes, more formerly known as polygons.
Sara Reyes
CSE 684
Spring 2012

2. LEARNING OBJECTIVES
First, to distinguish between
convex and concave polygons.
Next, to distinguish between
regular and irregular polygons.
Lastly, to classify polygons
according to how many sides
they have.

3. WHAT ARE POLYGONS?
Closed shapes or figures in a plane with three or more
sides.
Alternatively, a polygon can be defined as a closed
planar figure that is the union of a finite number of line
segments.
The term polygon is derived from a Greek word
meaning “many-angled”.

4. CONVEX VS. CONCAVE
POLYGONS
Convex polygon- A Concave polygon- A
polygon for which any two polygon that is not convex. A
interior points can be line segment connecting two
connected by a line segment points may pass outside the
that stays entirely inside the figure.
polygon.

5. WHAT HAVE WE COVERED SO
FAR?
 Distinguish between convex and concave polygons
Distinguish between regular and irregular polygons
Classify polygons according to the number of sides
they have
o classify polygons according to how many they
have

6. REGULAR VS. IRREGULAR
POLYGONS
An irregular polygon is a
polygon whose sides are not
A regular polygon is a the same length or whose
polygon in which all the interior angles do not all
angles and sides are equal. have the same measure.

7. SO, WHAT HAVE WE COVERED SO
FAR?
 Distinguish between convex and concave polygons
 Distinguish between regular and irregular polygons
Classify polygons according to the number of sides they
have
o classify polygons according to how many they have

8. WHAT IS A TRIANGLE?
A triangle, sometimes called a trigon, is a three-sided
polygon.

9. WHAT IS A QUADRILATERAL?
A quadrilateral is a four-sided polygon.

10. WHAT IS A PENTAGON?
A pentagon is a five-sided polygon.

11. WHAT IS A HEXAGON?
A hexagon, also referred to as a sexagon, is a
six-sided polygon.

12. WHAT IS A HEPTAGON?
A heptagon, also referred to as a septagon, is a
seven-sided polygon.

13. WHAT IS A OCTAGON?
An octagon is a eight-sided polygon.

14. WHAT IS A NONAGON?
A nonagon is a nine-sided polygon.

15. WHAT IS A DECAGON?
A decagon is a ten-sided polygon.

16. SO, WHAT HAVE WE COVERED SO
FAR?
 Distinguish between convex and concave polygons
 Distinguish between regular and irregular polygons
 Classify polygons according to the number of sides they have
o classify polygons according to how many they have
Lets recap what we learned throughout this lesson…

17. RECAP OF WHAT WE LEARNED…
 A polygon is a closed figure with three (or more)
sides.
 When any two interior points of a polygon are
connected by a line segment that:
 stays entirely inside, it is a convex polygon
 passes outside, it is a concave (“caved in”) polygon
 Regular polygons have equal side lengths and
equal interior angle measures whereas irregular
polygons do not.
 Polygons can be classified by the number of sides:
 three-sided = triangle
 four-sided = quadrilateral
 five-sided = pentagon
 etc.

18. FACTS
Definitions:
Polygons- Cliffs Quick Review: Geometry, 2001 (pg. 55)
Convex- Cliffs Quick Review: Geometry, 2001 (pg. 191)
Concave- Cliffs Quick Review: Geometry, 2001 (pg. 191)
Regular-
http://www.mathatube.com/polygons-list-of-regular-
polygons.html
Irregular-
http://www.mathatube.com/polygons-list-of-regular-
polygons.html
Classification:
Cliffs Quick Review: Geometry, 2001 (pg. 57 )
Naming Polygons (by how many sides):
http://en.wikipedia.org/wiki/Polygon#Classification

19. IMAGES
Triangles:
http://labspace.open.ac.uk/mod/resource/view.php?id=420267
Quadrilaterals:
http://students-math-worksheets.blogspot.com/
Pentagons:
http://share.ehs.uen.org/node/11675
Hexagons:
http://share.ehs.uen.org/node/11675
Heptagons:
http://share.ehs.uen.org/node/11675
Octagons:
http://share.ehs.uen.org/node/11675
Nonagon:
http://discomath.etown.edu:8080/webMathematica/Definitions/Nonagon.
html
Decagon:
http://commons.wikimedia.org/wiki/File:Decagon_(PSF).png

20. Convex/Concave Polygon (Introduction):
http://www.emanueleferonato.com/images/convex_concave.png
Regular/Irregular Polygon (Introduction):
http://www.wyzant.com/Help/Images/polygon1.gif
Convex/Non-Convex Polygons (Body):
http://www.onemathematicalcat.org/Math/Geometry_obj/quadrilaterals.h
tm
Regular Polygons (Body):
http://www.mathatube.com/polygons-list-of-regular-polygons.html
Irregular polygons (Body):
http://www.matsuk12.us/176120115181252763/blank/browse.asp?a=38
3&BMDRN=2000&BCOB=0&c=66509
“The End” (Final Slide):
http://4.bp.blogspot.com/_EGnqH5_FsgU/TCvJHYZBG-
I/AAAAAAAABsI/F250wMkUBG0/s400/not-the-end.jpg