Download 1.6 Classify Polygons

1.6 Power Point Guide
Polygon
(Poly – means “many”)
So…a polygon is a many sided closed figure.
Examples:
1.6 Power Point Guide
Let’s categorize…..
(dents/no dents)
A type of polygon
with no dents
A closed figure that is
“many” sided
A type of polygon
with dents
(“think cave”)
EXAMPLE 1
Identify polygons
Tell whether the figure is a polygon and whether it is
convex or concave.
a.
b.
c.
d.
SOLUTION
a.
Some segments intersect more than two segments,
so it is not a polygon.
b.
The figure is a convex polygon.
c.
Part of the figure is not a segment, so it is not a
polygon.
d. The figure is a concave polygon.
# of sides
3
4
5
6
7
8
9
10
12
n
Type of Polygon
triangle
quadrilateral
pentagon
hexagon
heptagon
octagon
nonagon
decagon
dodecagon
n-gon
What is a polygon with 199 sides called? 199-gon
All sides are
equal.
Think “lateral” –
like a lateral pass
in football
All the sides are equal
and all the interior angles
are equal.
All the interior angles
are equal.
Here are some examples:
EXAMPLE 2
Classify polygons
Classify the polygon by the number of sides. Tell
whether the polygon is equilateral, equiangular, or
regular. Explain your reasoning.
a.
b.
SOLUTION
a.
The polygon has 6 sides. It is equilateral and
equiangular, so it is a regular hexagon.
b. The polygon has 4 sides, so it is a quadrilateral. It
is not equilateral or equiangular, so it is not
regular.
EXAMPLE 2
Classify polygons
Classify the polygon by the number of sides. Tell
whether the polygon is equilateral, equiangular, or
regular. Explain your reasoning.
c.
c.
The polygon has 12 sides, so it is a dodecagon.
The sides are congruent, so it is equilateral. The
polygon is not convex, so it is not regular.
EXAMPLE 3
Find side lengths
ALGEBRA 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
First, write and solve an equation to find the value of x.
Use the fact that the sides of a regular hexagon are
congruent.
3x + 6 = 4x – 2
Write equation.
6 =
x–2
Subtract 3x from each side.
8 = x
Add 2 to each side.
EXAMPLE 3
Find side lengths
Then find a side length. Evaluate
one of the expressions when x = 8.
3x + 6 = 3(8) + 6 = 30
ANSWER
The length of a side of the table is
30 inches.
GUIDED PRACTICE
for Example 3
3. The expressions 8y° and ( 9y – 15 )° represent the
measures of two of the angles in the table in
Example 3. Find the measure of an angle.
SOLUTION
First , write and solve an equation to find the value
of y. Use the fact that that the angles of a regular
hexagon are congruent.
8y = 9y – 15
0 = y – 15
15 = y
Write equation
Subtract each side by 8y
Add 15 to each side
GUIDED PRACTICE
for Example 3
Then find an angle. Evaluate one the expression
when y = 15°
8y = 8 · 15° = 120°
ANSWER
The measure of an angle is 120°
Fly Swatter Game!!!!
Fly swatter is a speed game that involves
speed thinking and speed swatting.
1pt
correct swat
1 pt correct explanation
Question 1
The answers two the following two questions are the same
1 and 2 are what kind of adjacent angles?
A and B are what kind of non-adjacent
angles?
A
B
Question 2
F and G are what kind of
angles?
Question 3
AED and BEC are what kind of
angles?
Question 4
AEB and BEC form a what?
Question 5
Find a concave hexagon.
Question 6
These are all what
kind of polygons?
Question 7
Name this polygon based on the
number of sides it has.
Question 8
What is the term for polygons
where all the ’s are congruent, but
the sides are not necessarily
equal?
Question 9
Name this polygon based on the
number of sides it has.
Question 10
This is what type of quadrilateral?
Question 11
This is a _______ quadrilateral.
Question 12
Find a convex heptagon
Question 13
What is the special name for a
polygon with an unknown number
of sides?
Question 14
Find a convex nonagon
Question 15
Base on the number of sides name
this polygon.
Question 16
Name this concave polygon.