1. 6.1 Vocabulary Side of a polygon Vertex of a polygon Diagonal
Regular polygon
Concave
convex

2. 6.1 Properties & Attributes of Polygons
Geometry

3. Polygon
Polygon- a plane figure that (1) is formed by 3 or more segments, such that no two sides with a common endpt are collinear and (2) each side intersects exactly 2 other sides , 1 at each endpt.
Means the figure is closed and no sides cross over each other.
Vertex- the endpts of each side
Think of them as the corner points!

4. For Ex.
vertex
side

5. Ex. 1 Is the figure a polygon?
yes
yes no no

6. KNOW THIS!!!!!!!!!!!! Number of sides 3 Type of polygon Triangle 45 6 7 8 9 10 12 n
Type of polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
N-gon

7. Special types of Polygons
Convex- no line that contains a side of a polygon goes through its interior
Concave- any part of a diagonal contains points from the exterior of the polygon
Equilateral- all sides are 
Equiangular- all angles are 
Regular polygon- equilateral and equiangular (convex)
(A regular polygon is always convex.)

8. Ex. 2 regular? ( ) ( )) ) ( ( ((
yes
NO!
NO!

9. Diagonals A (ie segments AE and AD) C B D E
Diagonal- a segment that joins 2 nonconsecutive vertices A
(ie segments AE and AD) C B D E

10. Thm 6-1-1 Polygon Angle Sum Theorem
The sum of the interior angle measures of a convex polygon with n sides is (n-2)180

11. Polygon
# of sides
# of triangles
Sum of interior angle measures
Triangle 3 1
180
Quadrilateral 4 2
360
Pentagon 5
540
Hexagon 6
720
n-gon n
n-2
(n-2)180

12. Interior  ‘s of a quad B A 1 2 m1+m2+m3+m4=360o 3 4 D C
The sum of the measures of the interior ‘s of a quad =360o. B A 1 2
m1+m2+m3+m4=360o 3 4 D C

13. Ex. 3 Find x ( X
x+x+55+55=360
2x+110=360
2x=250
X=125
55o ) X

14. Ex. 4
A. Find the sum of the interior angle measures of a convex heptagon.
B. Find the measure of each interior angle of a regular 16-gon.
C. Find the measure of each interior angle of pentagon ABCDE.
Ex.3

15. Assignment