1. Polygons and Classifying Polygons

2. (no gaps between the sides)
Polygons: Any shape with straight edges that is closed and has more than three SIDES. Each endpoint is a VERTEX of the polygon.
Each Polygon must be CLOSED
(no gaps between the sides)
To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counter clockwise direction. B A C D E
Polygon
NOT a Polygon
The name of the polygon above is ABCDE, BCDEA, DCBAE, etc.

3. any polygon that has 4 sides
Ex. 1 Name the polygon. Then identify its vertices, sides, and angles. X Y
Quadrilateral:
any polygon that has 4 sides Z U
Polygon Name: XYUZ
Vertices: X, Y, Z, U
Sides: XY, YU, UZ, ZX
Angles:  X,  Y,  Z,  U

4. Ex. 2 Is the figure a polygon? Explain. a) b) c) d)
Yes, polygon is formed by 5 straight line segments
No, all sides are not line segments
No, it is not “closed”
Yes, polygon is formed by 7 straight line segments

5. Classifying Polygons
You can classify a polygon by the number of sides it has.
The table below shows the names of some common polygons.
Sides
Name 3
Triangle 4
Quadrilateral 5
Pentagon 6 7
Hexagon
Heptagon 8
Octagon 9
Nonagon 10 11
Decagon
Undecagon 12
Dodecagon N
N - gon

6. Convex or Concave You can classify polygons as Convex or Concave:
Convex Polygon: No line that contains a side of the polygon passes through the interior of the polygon.
Concave Polygon: At least one line extended side passes through the interior.
Convex
Concave

7. Ex. 3 Classify the polygon by its sides
Ex Classify the polygon by its sides. Identify each as convex or concave.
Pentagon
Convex
Decagon
Concave

8. Equilateral Polygon Equiangular Polygon Regular Polygon
A polygon is equilateral, if all the sides are congruent.
A polygon is equiangular, if all its interior angles are congruent.
A polygon is regular if it is both equilateral and equiangular
Equilateral Polygon
Equiangular Polygon
Regular Polygon

9. Ex. 4 The polygon is equiangular. Find the value of x.
6xo
240o
6x = 240
Equiangular polygon
x = 240 6
x = 40o

10. Ex. 5 Polygon is regular. Find the value of x.20
7x - 1 = 20
Regular polygon
7x = 21
x = 21 7
x = 3 units

11. Class Work
Pg 306 #3– 5, #8 – 10
Pg 413 – 415 #2 – 21, 27, 36 – 38

12. Interior Angles and Exterior Angles

13. Polygon Interior Angles Theorem:
The sum of the measure of the interior angles of a convex polygon with N sides is _____________
(n – 2) ∙ 180o

14. Ex. 1 Determine the sum of the interior angles of a
a. 16 – sided polygon
b. 25 – sided polygon
(16 – 2) ∙ 180o
Poly. int. angles thm
= (14) ∙ 180o
= 2520o
(25 – 2) ∙ 180o
Poly. int. angles thm
= (23) ∙ 180o
= 4140o

15. Ex. 2 How many sides does a polygon if the sum of its interior angles is 3420o?
Polygon interior angles theorem
(n – 2) =
180
(n – 2) = 19
n =
n = 21 sides

16. Ex. 3. Write an equation for the sum of the interior angles
Ex. 3 Write an equation for the sum of the interior angles. Then solve for x.
Determine the sum of the interior angles.
Polygon interior angles theorem
(4 – 2) ∙ 180o
= (2) ∙ 180o
= 360o
Solve for x.
(2x – 15) + x + (2x – 15) + x = 360
6x – 30 = 360
6x = 390
x = __ 6
x = 65

17. Polygon Exterior Angles Theorem:
The sum of the measures of the exterior angles of a convex polygon is always __________
360o A B C D E

18. Ex. 4 Find the measure of an exterior angle for each regular convex polygon. a) 20 sides b) 15 sides
let x = measure of the exterior angle
20x = 360
Poly ext angles thm
x = __360___ 20
x = 18o
let x = measure of the exterior angle
15x = 360
Poly ext angles thm
x = __360___ 15
x = 24o

19. Ex. 5 Determine the value of x.
x + 9x = 360
Poly ext angles thm
x = 360
17x =
17x = 255
x = __255___ 17
x = 15

20. Class Work
Page 418 #2,4
Page 420 #4-7
Page 421 #8–24 (even)
Page 423 #1-8