Download notes 1.6

1.6 Classifying Polygons
Polygon:
A closed plane figure
! Formed by three or more line segments,
called sides.
! Each side intersects two other sides at the
endpoints, nowhere else.
! No two sides sharing an endpoint are
collinear.
!
The endpoint of a side is called a vertex.
! (Vertices is the plural form.)
!
Concave
vs.
Convex
Every diagonal is in the interior of the figure.
(Non convex)
!
!
Diagonal: a segment connecting
two non consecutive vertices.
Consecutive: one right after the other.
A rubber band fits the exact shape of a convex polygon. A concave polygon is “caved” in and will not have the same shape as the rubber band placed around it.
convex
concave
concave
convex
Not a polygon:
no sides Not a plane figure
Not
closed
List all the polygons you can
name; include the number of
sides.
3
triangle
30 sides: ! 4
quadrilateral
30-gon
! 5
pentagon
19 sides:
! 6
hexagon
19-gon
! 7
heptagon
108 sides: ! 8
octagon
108-gon
! 9
nonagon
! 10
decagon When you are asked to “classify a polygon,”
! 11-gon
you are expected to give one of these names.
! 12
dodecagon
! N
n-gon
!
Classify these polygons.
pentagon
Dodecagon
Heptagon
quadrilateral
Equilateral: Having sides of equal length.
Equiangular: Having angles of equal measure.
Regular:
Both equilateral and equiangular.
Are any of the above figures equilateral, equiangular, or regular?
How can we know?
These hatch marks indicate sides of equal length.
Classify the polygon shown at the right by the
number of sides. Explain how you know that the
sides of the polygon are congruent and that the
angles of the polygon are congruent.
Regular quadrilateral
Four sides of equal length (equilateral.)
Four angles that are each 90 degrees (equiangular.)
ALGEBR
A table is shaped like a
regular hexagon.The expressions
shown represent side lengths of the
hexagonal table. Find the length of a
side.
SOLUTION
3x +
=
6
8
=
=
4x –
x–
x
Write equation.
Subtract 3x from each side.
Add 2 to each side.
Then find a side length. Evaluate one of the expressions when x = 8.
3x +
ANSWE
=
3(8) +
=
3
The length of a side of the table is 30
Geometry
!
Page 44(2-7, 8-16 ev, 18-23,24-30 ev, 33-36)
!
There is only one section left in chapter one.
Begin studying for the test over the whole
chapter. There have been a lot of new
definitions and concepts.