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CHAPTER 3: PARALLEL
LINES AND PLANES
Section 3-5: Angles of Polygons
POLYGONS
Polygons are formed by coplanar segments
(sides) where:
1. Each segment (side) intersects
exactly two other segments, one at
each endpoint.
2. No two segments (sides) with a
common endpoint are collinear.
POLYGONS
Polygons
Not Polygons
CLASSIFYING POLYGONS
Polygons are classified according to the
number of sides they have.
3 sides
4 sides
5 sides
6 sides
8 sides
10 sides
triangle
quadrilateral
pentagon
hexagon
octagon
decagon
POLYGON VOCABULARY
• We refer to polygons by listing its vertices in
consecutive order.
• A diagonal of a polygon is a segment that joins
two nonconsecutive vertices.
• We can find the sum of the measures of the
interior angles of a polygon by drawing all
diagonals from one vertex.
POLYGON
1. What type of polygon is shown?
A hexagon
2. Name the polygon.
Hexagon ABCDEF
3. Draw the diagonals
of the polygon.
A
B
F
C
E
D
POLYGON MEASURES
Since we know that the sum of the
measures of the interior angles of
a triangle is 180, we can find the
measure of polygons by
determining how many triangles it
contains.
POLYGON MEASURES
Consider the following polygons:
Triangle
3 sides
1 triangle
180(1)=
180
Quadrilateral
4 sides
2 triangles
180(2) =
360
Pentagon
5 sides
3 triangles
180(3)=
540
Hexagon
6 sides
4 triangles
180(4)=
720
THEOREMS
Theorem 3-13:
The sum of the measures of the interior
angles of a convex polygon with n sides is
(n – 2)180.
Theorem 3-14:
The sum of the measures of the exterior
angles of any convex polygon, one angle
at each vertex, is 360.
POLYGON SPECIFICS
Polygons can be:
•
Equiangular
•
Equilateral
•
Both equiangular and equilateral
(Regular Polygons).
REGULAR POLYGONS
Take the following scenarios into account:
120
120
120
120
120
120
120
120
120
120
Not equiangular
nor equilateral
120
Equiangular
Equilateral
120
Regular
CLASSWORK/HOMEWORK
• Pg. 103, Classroom Exercises 1-9
• Pg. 104, Written Exercises 2-20 even