1. G4.1 Introducing Polygons
Objectives:
Define “polygon”
Classify polygons by their sides
Classify polygons by their angles.
Discover the sum of the interior angles of any polygon
Use the Polygon-Sum conjecture to solve for missing angles

2. Concept: Define Polygon
POLYGON: A 2-dimensional object made of line segments connected at their endpoints to enclose an area.
POLYGONS
NOT POLYGONS

3. Concept: Define Concave & Convex
CONVEX: Any polygon that has all of it’s verticies pointing
away from the interior
of the polygon
ON A PEGBOARD, A RUBBER BAND WILL COPY THE CONVEX SHAPE
CONCAVE: Any polygon that has a vertex that points to the
interior of the polygon.

4. Concept: NAMES OF POLYGONS
SIDES Name
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
N n-gon

5. Concept: Classify by sides and angles
Equilateral: All sides are equal
Equiangular: All angles are equal
Regular: All angles are equal and all
sides are equal.
This is just like a triangle classification.

6. Concept: How Many Diagonals?
FIND THE NUMBER
DIAGONALS CAN BE FORMED FROM A SINGLE VERTEX IN ANY POLYGON?
6 SIDES = 3 DIAGONALS

7. Concept: How Many Diagonals?
TRY AGAIN. CAN YOU MAKE A CONJECTURE ABOUT THE RELATIONSHIP BETWEEN THE NUMBER OF SIDES IN THE POLYGON AND THE NUMBER OF DIAGONALS FROM ONE VERTEX?
8 SIDES =
5 DIAGONALS
DIAGONALS = N – 3

8. Concept: How Many TRIANGLES?
FIND THE NUMBER
OF TRIANGLES FORMED BY DIAGONALS FROM ONE VERTEX
8 SIDES =
6 TRIANGLES

9. Concept: How Many TRIANGLES?
IS THERE A RELATIONSHIP BETWEEN THE NUMBER OF SIDES IN A POLYGON AND THE NUMBER OF TRIANGLES CREATED?
8 SIDES =
6 TRIANGLES
TRIANGLES = N – 2

10. Concept: How Many DEGREES?
HOW MANY DEGREES ARE IN EVERY TRIANGLE?
HOW MANY TRIANGLES IN THE POLYGON?
CAN YOU MAKE A CONJECTURE or FORMUL ABOUT THE SUM OF THE DEGREES IN A POLYGON?
4 SIDES = 2 TRIANGLES

11. CONCEPT: POLYGON SUM CONJECTURE
EACH TRIANGLE HAS 180° IF N IS THE NUMBER OF SIDES OF A POLYGON THEN: INTERIOR ANGLE SUM = (N–2)180º

12. 2 3 1 4 5
INT ANGLE SUM = ( 5 – 2 ) 180°
( 3 ) 180° = 540°

13. CONCEPT: REGULAR POLYGONS
REGULAR POLYGONS HAVE EQUAL SIDES AND EQUAL ANGLES SO WE CAN FIND THE MEASURE OF EACH INTERIOR ANGLE

14. N EACH INTERIOR ANGLE OF A REGULAR POLYGON = (N – 2 ) 180
REMEMBER N = NUMBER OF SIDES

15. REGULAR HEXAGON
INT ANGLE SUM =
(6 – 2 ) 180 = 720°
EACH INT ANGLE =
720 = 120° 6

16. CONCEPT: Using Polygon-Sum
Find the measures of
g and h.
Quadrilateral
Sum = 360º
Pentagon
Sum = 540º

17. CONCEPT: Using Polygon-Sum
– –225
3g = 315
___ ___
g = 105º

18. CONCEPT: Using Polygon-Sum
A circle has 360º
x = 360º
238 + x = 360º
– –238
x = 122º

19. CONCEPT: Using Polygon-Sum
h = 360º
278 + h = 360º
122º
– –278
h = 82º

20. Concept: Polygon Diagonal Sum Conj.
Remember worksheet 5.1 where you had to find the number of diagonals of a polygon. Counting proved to be difficult. WE DIDN’T DO THAT PART!!
It would prove to be time consuming and difficult

21. d = n(n–3) 2 Concept: Polygon Diagonal Sum Conj.
GOOD NEWS!!! There’s an App for that!!!
Okay, not realy. But there is an equation.
d = n(n–3) 2
Check it out:
D = 6(6-3) = 6(3) = = 9

22. Homework:
PM G4.1