Download - Polygons
POLYGONSUnderstanding 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 ReyesCSE 684Spring 2012
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.
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”.
CONVEX VS. CONCAVE POLYGONS
Convex polygon- A polygon for which any two interior points can be connected by a line segment that stays entirely inside the polygon.
Concave polygon- A polygon that is not convex. A line segment connecting two points may pass outside the figure.
“CAVED IN”
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
REGULAR VS. IRREGULAR POLYGONS
A regular polygon is a polygon in which all the angles and sides are equal.
An irregular polygon is a polygon whose sides are not the same length or whose interior angles do not all have the same measure.
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
WHAT IS A TRIANGLE?
A triangle, sometimes called a trigon, is a three-sided polygon.
WHAT IS A QUADRILATERAL?
A quadrilateral is a four-sided polygon.
WHAT IS A PENTAGON?
A pentagon is a five-sided polygon.
WHAT IS A HEXAGON?
A hexagon, also referred to as a sexagon, is a six-sided polygon.
WHAT IS A HEPTAGON?
A heptagon, also referred to as a septagon, is a seven-sided polygon.
WHAT IS A OCTAGON?
An octagon is a eight-sided polygon.
WHAT IS A NONAGON?
A nonagon is a nine-sided polygon.
WHAT IS A DECAGON?
A decagon is a ten-sided polygon.
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 haveo classify polygons according to how many they have
Lets recap what we learned throughout this lesson…
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.
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
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
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.htm
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=383&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