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 "manyangled"
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:

ConvexA 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:
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.  13agon, 15agon 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.
2) The vertices of a polygon are the points where its sides intersect.
Equilangular All the angles of a polygon are equal.
Equilateral All the sides of a polygon are equal. In this example, a,b, and c are equal so this is an equilateral triangle.
Regular both the angles and the sides of a polygon are equal
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
 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 ngon is an expression for any number over 12 (ex. A polygon with 13 sides= 13gon) *11 is expection to this rule, 11 is an 11gon
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
4x2 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.
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*
 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
 An ngon is an expression for any number over 12 (ex. A polygon with 13 sides= 13gon)
*11 is expection to this rule, 11 is an 11gon*
Practice Problems:
1. Tell whether the polygon is regular, equiangular, or equilateral. Explain your reasoning.
a)
regularpolygon.jpg
b)
gs_157.PNG.png
c)
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
4x2 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.
Mrs Clark's Suggested Problems:
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 "manyangled"
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:

ConvexA 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:
dont have a specific name.
i.e.  13agon, 15agon 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.
2) The vertices of a polygon are the points where its sides intersect.
Equilangular All the angles of a polygon are equal.
Equilateral All the sides of a polygon are equal. In this example, a,b, and c are equal so this is an equilateral triangle.
Regular both the angles and the sides of a polygon are equal
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
 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.
 An ngon is an expression for any number over 12 (ex. A polygon with 13 sides= 13gon)
*11 is expection to this rule, 11 is an 11gon
Practice Problems:
1. Tell whether the polygon is regular, equiangular, or equilateral. Explain your reasoning.
a)
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
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.
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*
 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.
 An ngon is an expression for any number over 12 (ex. A polygon with 13 sides= 13gon)
*11 is expection to this rule, 11 is an 11gon*
Practice Problems:
1. Tell whether the polygon is regular, equiangular, or equilateral. Explain your reasoning.
a)
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
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.