Mrs Clark's Suggested Problems:

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Identifying and Classifying Polygons


-Reference Chapter 1.6-
Identifying a Polygon
-A polygon is a closed plane figure with the following properties

by. Elena F., maggie r., Cori M.
POLYGONS

1. the greek meaning for poly gon is "many-angled"

2. polygons are formed by 3 or more SEGMENTS, called sides such that no 2 sides w/a common endpoint are collinear.

3. There are two different categories of polygons which are the following:

-

Convex-A convex polygon has all the angles pointing away from the inside.
-
Non convex
: sometiems referred to as concave. In this polygon one or more of the angles are pointing inward.
For a mental image, here are some examples of each:

external image 18136.nfg001.jpg
number of sides
type of polygons
3
triangle
4
quadrilateral
5
pentagon
6
hexagon
7
heptagon
8
octagon
9
nonagon
10
decagon
12
dodecagon
all other numbers
dont have a specific name.
i.e. - 13-agon, 15-agon ect..


Identifying and Classifying Polygons!
By: Lizzie L., Erin S., and Holly F. Friday Per. 1

1) The vertex of an angle is the point where the two rays that form the angle intersect.

external image IMG00056.GIF
2) The vertices of a polygon are the points where its sides intersect.






external image IMG00057.GIF

Equilangular- All the angles of a polygon are equal.
external image Equiangular%20Polygon2.jpg
Equilateral- All the sides of a polygon are equal. In this example, a,b, and c are equal so this is an equilateral triangle.
external image equilateral_triangle_image.png



Regular- both the angles and the sides of a polygon are equal

external image triangles%20-%20all%20equal%20sides.JPG
PRACTICE PROBLEMS
1. A polygon has 3 sides. Side a=14, side b=27, and side c=36. Is this equilateral?
Answer
: No. A polygon is only equilateral is all the sides are the same length.
2. A polygon has 4 sides. a=3, b=3, c=3, d=3. All 4 angles are right angles. Is this regular?
Answer
: Yes because if all the sides are equal and all the angles are equal then the polygon is regular.
3. A polygon has 3 angles. a=5, b=5, and c=5. Is it equiangular?
Answer
: Yes because all the angles are the same.


Holli H. Madi S. Kelly L. Gabi L. Period 2  By: Rose Hutchison, Jackie McGee, Shaeffer Smith, and Grace Spencer (Friday Period 4)What is a Polygon?

A polygon is a closed plane figure with the following properties:
1.) It is formed by three or more line segments called sides.
2.) Each side intersects exactly two sides, one at each endpoint, so that no two sides with a common endpoint are collinear.

-It is formed by 3 or more line segments called sides.
-Each side intersects two sides, one at each endpoint, so that no two sides with a common endpoint are collinear.
-Lines must be straight line segments, not curved of wavy.
*CIRCLES ARE NOT POLYGONS

http://www.google.com/imgres?imgurl=http://www.mathatube.com/images/polygons_1_.jpg&imgrefurl=http://www.mathatube.com/polygons-list-of-regular-polygons.html&usg=__hxoIXrpLCk-n7WbPx57ihWL9EfY=&h=310&w=480&sz=30&hl=en&start=0&zoom=1&tbnid=zTLMtDIpM4IBLM:&tbnh=104&tbnw=161&prev=/images%3Fq%3Dpolygons%26hl%3Den%26safe%3Dactive%26biw%3D1003%26bih%3D433%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=220&ei=0HeGTMiGNIu1ngegybnKAQ&oei=u3eGTKKODsiRnwfwjqW1Dg&esq=5&page=1&ndsp=10&ved=1t:429,r:5,s:0&tx=70&ty=63
http://www.google.com/imgres?imgurl=http://www.mathatube.com/images/polygons_1_.jpg&imgrefurl=http://www.mathatube.com/polygons-list-of-regular-polygons.html&usg=__hxoIXrpLCk-n7WbPx57ihWL9EfY=&h=310&w=480&sz=30&hl=en&start=0&zoom=1&tbnid=zTLMtDIpM4IBLM:&tbnh=104&tbnw=161&prev=/images%3Fq%3Dpolygons%26hl%3Den%26safe%3Dactive%26biw%3D1003%26bih%3D433%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=220&ei=0HeGTMiGNIu1ngegybnKAQ&oei=u3eGTKKODsiRnwfwjqW1Dg&esq=5&page=1&ndsp=10&ved=1t:429,r:5,s:0&tx=70&ty=63


http://www.google.com/imgres?imgurl=http://www.mathatube.com/images/polygons_1_.jpg&imgrefurl=http://www.mathatube.com/polygons-list-of-regular-polygons.html&usg=__hxoIXrpLCk-n7WbPx57ihWL9EfY=&h=310&w=480&sz=30&hl=en&start=0&zoom=1&tbnid=zTLMtDIpM4IBLM:&tbnh=104&tbnw=161&prev=/images%3Fq%3Dpolygons%26hl%3Den%26safe%3Dactive%26biw%3D1003%26bih%3D433%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=220&ei=0HeGTMiGNIu1ngegybnKAQ&oei=u3eGTKKODsiRnwfwjqW1Dg&esq=5&page=1&ndsp=10&ved=1t:429,r:5,s:0&tx=70&ty=63

- REGULAR POLYGONS are equilateral (all sides are same length) and equiangular (all angles are equal in degree)
http://www.bing.com/images/search?q=polygons&FORM=BIFD#focal=73ba3b72eb495b741bcbc5cd07620773&furl=http%3A%2F%2Fvisual.merriam-webster.com%2Fimages%2Fscience%2Fscientific-symbols%2Fgeometrical-shapes%2Fpolygons_1.jpg
http://www.bing.com/images/search?q=polygons&FORM=BIFD#focal=73ba3b72eb495b741bcbc5cd07620773&furl=http%3A%2F%2Fvisual.merriam-webster.com%2Fimages%2Fscience%2Fscientific-symbols%2Fgeometrical-shapes%2Fpolygons_1.jpg

- A polygon is convex if no line that contains a side of a polygon contains a point in the interior of the polygon. A polygon is concave if one or more lines containing a side of the polygon contains a point on the interior of the polygon.


ConvexPolygon_1000.gif
ConvexPolygon_1000.gif

ConvexPolygon_1000.gif

- An n-gon is an expression for any number over 12 (ex. A polygon with 13 sides= 13-gon)
*11 is expection to this rule, 11 is an 11-gon
external image convexconcave.gif

Practice Problems:

1. Tell whether the polygon is regular, equiangular, or equilateral. Explain your reasoning.

a)

regularpolygon.jpg
regularpolygon.jpg

regularpolygon.jpg
b)
gs_157.PNG.png
gs_157.PNG.png

gs_157.PNG.png
c)
triangle_class5.gif
triangle_class5.gif

triangle_class5.gif


Answers:
a) Regular, all sides and angles are the same
b) Equiangular, angles are all the same, sides are different
c) Equilateral, all sides are the same, angles could be different.

2. A table is shaped like a regular hexagon. The expressions show represent side lengths of the hexagonal table. Find the length of each side.
3x+6 in

11.GIF.gif
11.GIF.gif

11.GIF.gif
4x-2 in


Answer:
3x + 6 = 4x - 2
-3x -3x
6= x - 2
+2 +2
8= x

3(8) + 6= 30
4(8) - 2= 30
The length of the sides is 30 inches.

Practice Problems (Cont):
1. Tell whether each figure is a regular polygon. If so, tell if it is concave or convex.
http://www.bing.com/images/search?q=polygons&FORM=BIFD#focal=9485f3d27fe3894b7f9959677f2a3aca&furl=http%3A%2F%2Fwww.georgehart.com%2Fvirtual-polyhedra%2Ffigs%2Fpolygons.gif
http://www.bing.com/images/search?q=polygons&FORM=BIFD#focal=9485f3d27fe3894b7f9959677f2a3aca&furl=http%3A%2F%2Fwww.georgehart.com%2Fvirtual-polyhedra%2Ffigs%2Fpolygons.gif


Answers: All figures are regular. 7/2 is concave, 7/3 is convex.

Holli H. Madi S. Kelly L. Gabi L. Period 2 Shaeffer S., Rose H., Grace S., Jackie M. Period 4
What is a Polygon?
=
A polygon is a closed plane figure with the following properties:
1.) It is formed by three or more line segments called sides.
2.) Each side intersects exactly two sides, one at each endpoint, so that no two sides with a common endpoint are collinear.

-It is formed by 3 or more line segments called sides.
-Each side intersects two sides, one at each endpoint, so that no two sides with a common endpoint are collinear.
-Lines must be straight line segments, not curved of wavy.
*CIRCLES ARE NOT POLYGONS*

http://www.google.com/imgres?imgurl=http://www.mathatube.com/images/polygons_1_.jpg&imgrefurl=http://www.mathatube.com/polygons-list-of-regular-polygons.html&usg=__hxoIXrpLCk-n7WbPx57ihWL9EfY=&h=310&w=480&sz=30&hl=en&start=0&zoom=1&tbnid=zTLMtDIpM4IBLM:&tbnh=104&tbnw=161&prev=/images%3Fq%3Dpolygons%26hl%3Den%26safe%3Dactive%26biw%3D1003%26bih%3D433%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=220&ei=0HeGTMiGNIu1ngegybnKAQ&oei=u3eGTKKODsiRnwfwjqW1Dg&esq=5&page=1&ndsp=10&ved=1t:429,r:5,s:0&tx=70&ty=63
http://www.google.com/imgres?imgurl=http://www.mathatube.com/images/polygons_1_.jpg&imgrefurl=http://www.mathatube.com/polygons-list-of-regular-polygons.html&usg=__hxoIXrpLCk-n7WbPx57ihWL9EfY=&h=310&w=480&sz=30&hl=en&start=0&zoom=1&tbnid=zTLMtDIpM4IBLM:&tbnh=104&tbnw=161&prev=/images%3Fq%3Dpolygons%26hl%3Den%26safe%3Dactive%26biw%3D1003%26bih%3D433%26gbv%3D2%26tbs%3Disch:1&itbs=1&iact=rc&dur=220&ei=0HeGTMiGNIu1ngegybnKAQ&oei=u3eGTKKODsiRnwfwjqW1Dg&esq=5&page=1&ndsp=10&ved=1t:429,r:5,s:0&tx=70&ty=63

- REGULAR POLYGONS are equilateral (all sides are same length) and equiangular (all angles are equal in degree)
- A polygon is convex if no line that contains a side of a polygon contains a point in the interior of the polygon. A polygon is concave if one or more lines containing a side of the polygon contains a point on the interior of the polygon.

ConvexPolygon_1000.gif
ConvexPolygon_1000.gif


- An n-gon is an expression for any number over 12 (ex. A polygon with 13 sides= 13-gon)
*11 is expection to this rule, 11 is an 11-gon*
external image convexconcave.gif
Practice Problems:

1. Tell whether the polygon is regular, equiangular, or equilateral. Explain your reasoning.

a)
regularpolygon.jpg
regularpolygon.jpg
b)
gs_157.PNG.png
gs_157.PNG.png
c)
triangle_class5.gif
triangle_class5.gif



Answers:
a) Regular, all sides and angles are the same
b) Equiangular, angles are all the same, sides are different
c) Equilateral, all sides are the same, angles could be different.

2. A table is shaped like a regular hexagon. The expressions show represent side lengths of the hexagonal table. Find the length of each side.
3x+6 in

11.GIF.gif
11.GIF.gif
4x-2 in



Answer:
3x + 6 = 4x - 2
-3x -3x
6= x - 2
+2 +2
8= x

3(8) + 6= 30
4(8) - 2= 30
The length of the sides is 30 inches.