Tuesday  September 20


REVIEW: Recall our previous discussions for a polygon with n sides.

In general: the sum of the interior angles in a n sided polygon is
                                      (n-2) *180 degrees.

A regular  polygon is a polygon where the sides are all of equal length and the angles are all congruent (or of equal measure).



In general: The individual angle for a regular polygon with n sides is (n-2)*180/n degrees.
This can be expressed in other ways using algebra:
(n-2)*180/n = [180 n - 360] / n = 180 - 360/n.




name of polygon n
degrees of the interior 
measure of each angle
360 degrees divided 
by # in Column 2
equilateral triangle 3
60  360 / 3 = 120
square 4
90  360/4= 90
regular pentagon 5
3*180/5= 108
360/5= 72
regular hexagon 6
4*180/6=120
360/6= 60
regular heptagon 7
5*180/7
360/7
regular octagon 8
6*180/8=135
360/8 = 45
regular dodecagon
12
10*180/12=1800/12=150
360/12=30




V*R     =   R2.
*
Id
R120
R240
V
G=R1
H=R2
Id
I





R120

R240

R1


R240

I

R2


V

R2
R1
I

R120
G=R1




I

H=R2





I
Do Activity on product of symmetries.
This shows that R240*V = R1

This "multiplicative" structure  is called the Group of symmetries of the equilateral triangle.

Given any figure we can talk about the group of its symmetries.
Does a figure always have at least one symmetry? .....

Yes... The Identity symmetry.
Such a symmetry is called the trival symmetry.