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