1.8
warm-up 2
Simplify the expression
6y-(2y-1)-4(3y+2)
a. -8y-7
b. -8y-3
c. -8y+1
d. -8y+7
2
Polygon Angle-Sum
Theorems
Pardekooper
Lets start with some
common terms.
• Polygon
– A closed plane figure with
at least three sides that
are segments. The sides
intersect only at their
endpoints, and no
adjacent sides are
collinear.
Pardekooper
Pardekooper
No,
No,
No,
two sides
it
is
not
it
has
Intersect
Yes
a
plane
Between
no
sides
figure
endpoints
Lets start with some
common terms.
• Regular Polygon
– All the sides are congruent
– All the angles are
congruent
Pardekooper
Name all the
polygons below
B
C
A
D
E
polygon ABCDE
polygon ABE
polygon BCDE
Pardekooper
Now name the parts
of the polygon
B
C
A
D
E
Vertices: A, B, C, D, E,
Sides: AB, BC, CD, DE, EA
Angles: A, B, C, D,E
Pardekooper
Lets name the
polygons
# of sides
name
3
4
triangle
quadrilateral
5
pentagon
6
hexagon
7
heptagon
8
octagon
9
nonagon
10
decagon
11
hendecagon
12
n
dodecagon
n-gon
Pardekooper
How about different types
of polygons
Convex polygons
no diagonal with points
outside the polygon
Pardekooper
How about different types
of polygons
Concave polygons
at least one diagonal
with points outside the
polygon
Pardekooper
Just two more theorems !
Polygon Angle-Sum Theorem
The sum of the measures of the
interior angles of a n-gon is
(n-2)180.
Example:
Find the sum of the measures
of the angles of a 15-gon.
formula:
Pardekooper
(n-2)180
(15-2)180
(13)180
2340
n = 15
1170
1000
x0
1050
Pardekooper
1150
5 sides
(5-2)180
Use the formula to
(3)180 find out how
540
How many
sides ?
many
degrees.
(n-2)180
Just one more theorem !
Polygon Exterior Angle-Sum
Theorem
The sum of the measures of the
exterior angles of a polygon, one at
each vertex is 360.
2
3
1
4
6
5
Pardekooper
m1 + m2 + m3 + m4 + m5 + m6 = 360