Download November 11, 2014

November 11, 2014
3.5 Polygons
poly means "many"
gon means "angles"
polygon means "many angles"
note that each polygon
is formed by coplanar segments (called sides)
such that:
each segment intersects exactly 2 other segments,
1 at each endpoint
no 2 segments with a common endpoint are collinear
are these all
polygons?
Why are these not polygons?
Convex polygons
How are these two groups of polygons different?
In our class and our book,
when we say polygon
we mean convex polygons
Non convex (concave) polygons
November 11, 2014
We classify polygons by
the number of sides....
Convex polygons
In our class and our book,
when we say polygon
we mean convex polygons
3
4
5
6
8
10
n
It is a polygon such that:
no line containing a side of the polygon
contains a point in the interior of the
polygon
D
C
E
A
B
WHEN
NAMING A
POLYGON,
YOU MUST
NAME THE
VERTICES IN
ORDER!!!!
triangle
quadrilateral
pentagon
hexagon
octagon
decagon
n-gon (or n-agon)
D
C
E
A
Diagonal
is a segment that joins
two non consecutive vertices
B
D
C
E
4 sides
2 triangles
angle sum = 2(180)
number of sides = 4
angle sum = (4-2)(180)
5 sides
3 triangles
angle sum = 3(180)
number of sides = 5
angle sum = (5-2)(180)
6 sides
4 triangles
angle sum = 4(180)
number of sides = 6
angle sum = (6-2)(180)
A
THM:
The sum of the measures of the
angles of a convex polygon withn
sides is (n-2)180.
B
now we'll do the triangle exterior angles activity
November 11, 2014
D
C
E
A
THM:
The sum of the measures of the
exterior angles of any convex
polygon, one angle at each angle,
is 360.
A polygon has 32 sides. Find
(a) the sum of the measures of the interior angles
and
(b) the sum of the measures of the exterior angles,
one at each vertexes
(a) interior angles sum
(32 - 2)180
5400
B
(b) exterior sum
360
Polygons can be equiangular or equilateral.
Polygons can be equiangular or equilateral.
hexagon that is neither
equiangular
or
equilateral.
120o
120o
120o
120o
120o
120o
Polygons can be equiangular or equilateral.
hexagon
that is
equiangular
Polygons can be equiangular or equilateral.
If a polygon is both equiangular or equilateral, it is
called a regular polygon.
120o
hexagon
that is
equilateral
120o
120o
120o
120o
120o
hexagon that is both
equiangular
and
equilateral,
thus regular.
November 11, 2014
A regular polygon has 12 sides.
Find the measure of each interior angle.
A regular polygon has 12 sides.
Find the measure of each exterior angle.
interior angles sum
(12 - 2)180
1800
exterior angles sum
360
each of 12 congruent exterior angles
360/12
30
each of 12 congruent interior angles
180 - 30
150
each of 12 congruent angles
1800/12
150
Find
(a) the sum of the measures of the interior angles,
and
(b) the sum of the measures of the exterior angles, one angle
at each vertex.
Find
(a) the sum of the measures of the interior angles,
and
(b) the sum of the measures of the exterior angles, one angle
at each vertex.
For a polygon with 7 sides.
For a 17-gon.
2700
360
900
360
Find the measure of an interior angle.
Find the measure of an interior angle.
for a regular octagon
for a regular quadrilateral
90
135
November 11, 2014
Find the measure of an interior angle.
Find the measure of an interior angle.
for a regular polygon with 20 sides
for a regular polygon with 15 sides
162
156
always
sometimes
Complete with always, sometimes , or never.
Complete with always, sometimes , or never.
The sum of the measures of the exterior angles of any
polygon, one angle at each vertex, is ________ 360.
The sum of the measures of the angles of a convex polygon is
________ 360.
sometimes
never
Complete with always, sometimes , or never.
Complete with always, sometimes , or never.
A segment joining two vertices of a polygon is ________ a
diagonal.
The sum of the measures of the exterior angles of any polygon
________ depends on the number of sides of the polygon.
November 11, 2014
sometimes
always
Complete with always, sometimes , or never.
Complete with always, sometimes , or never.
An equiangular polygon is ________ regular.
A regular polygon is ________ equilateral.
180
360
3240
360
Find the interior angle sum and the exterior angle sum for:
Find the interior angle sum and the exterior angle sum for:
a triangle
a 20-gon
4500
360
36
Find the interior angle sum and the exterior angle sum for:
Complete.
a 27-gon
The exterior angle of a regular polygon has measure 10. The
polygon has _________ sides.
November 11, 2014
18
Complete.
The interior angle of a regular polygon has measure 160. The
polygon has _________ sides.
95
Complete.
Three of the angles of a quadrilateral have measures 90, 60, and
115. The fourth angle has measure _________.