Warm-Up: Copy and
Complete
• The last day to turn in ANY late or missing work is
______________________.
• All test re-takes must be taken ________________ or
during PACK this week.
• Define Quadrilateral
Polygon classification
1.
Homework: p 386 #1-15, 23-33 odd
Concave Polygon
Convex Polygon
Classifying Polygons
2. Naming Polygons based on the number of sides:
3 sides = Triangle
(This label is based on the number of angles.)
4 sides = Quadrilateral
5 sides = Pentagon
6 sides = Hexagon
7 sides = Heptagon
8 sides = Octagon
9 sides = Nonagon
10 sides = Decagon
Polygons
Triangle - A polygon with three sides.
Polygons
Quadrilateral - A polygon with four sides.
Polygons
Parallelogram - A quadrilateral with two pairs of
parallel sides.
Polygons
Trapezoid - A quadrilateral which has one pair of
parallel sides.
Polygons
Rectangle - a quadrilateral with four congruent
angles (all 90°).
Polygons
Rhombus - A parallelogram with four congruent
sides.
Polygons
Square - a quadrilateral with four congruent sides
and four congruent angles (all 90°).
Polygons
Pentagon - A polygon with five sides.
Polygons
Hexagon - A polygon with six sides.
Polygons
Octagon - A polygon with eight sides.
Polygons
Decagon - A polygon with ten sides.
Bell Work
5 minutes
3. How do you find the sum of the interior angles of an n-gon?
Sum of
Interior
Angles
 180  (n  2)
Polygon Practice
3. Find the sum of the interior angles of the following polygons.
Hexagon:
22-gon
Hexagon
22-gon
Sum of Interior  180  (n  2)
Angles
Sum of Interior
 180  (n  2)
Angles
Sum of Interior
 180  (6  2)
Angles
Sum of Interior
 180   4
Angles
Sum of Interior
 180  ( 22  2)
Angles
Sum of Interior
 180   20
Angles
Sum of Interior
 720 
Angles
Sum of Interior
 3600 
Angles
Polygon practice
3. What does “sum of the interior angles” mean?
The answer when I add up
all of the angles on the
INSIDE of a polygon.
Polygon practice
4. What is a regular polygon?
All of the angles are the
congruent (same measure) and
all of the sides are congruent
(same length).
Polygon practice
3. How do you find the measure of an (each/one) interior angle of
a regular n-gon?
Measure of One
Interior angle of a 
Regular n-gon
180  ( n  2)
n
Polygon practice
3. Find the measure of each interior angle of the following polygons.
Hexagon:
Nonagon
Hexagon
Nonagon
Measure of one 180  ( n  2)

Interior Angle
n
Measure of one 180  (6  2)
Interior Angle 
6
Measure of one 180  4
Interior Angle 
Measure of one 180  ( n  2)

Interior Angle
n
Measure of one 180  (9  2)
Interior Angle 
9
Measure of one 180  7
Interior Angle 
Measure of one
Interior Angle  120 
Measure of one
Interior Angle  140 
6
Measure of one
720
Interior Angle 
6
9
Measure of one 1260
Interior Angle 
9
Polygon practice
4. What is the sum of the exterior angles of any regular polygon?
The sum of the measures
of the exterior angles of
any polygon is always
.
360
Polygon practice
4. How do you find the measure of one exterior angle of a regular
polygon?
Measure of One
Exterior angle of
a Regular n-gon
360

n
Polygon practice
6. Find the measure of an exterior angle of the following regular polygons.
Decagon
Measure of one
Exterior Angle
Measure of one
Exterior Angle
Measure of one
Exterior Angle
360

n
360

10
 36
Pentagon
360

n
Measure of one
360
Exterior Angle 
5
Measure of one
Exterior Angle
Measure of one
Exterior Angle
 72
Polygon practice
7. Find the number of sides for a regular polygon using the information
given:
a) The measure of each exterior angle is 30 degrees.
360
 30
n
360
n
 30  n
n
360
n
30
10  n
Polygon practice
7. Find the number of sides for a regular polygon using the information
given:
b) The measure of each interior angle is 135 degrees.
( n  2)  180
 135
n
Polygon practice
7. Find the number of sides for a regular polygon using the information
given:
a) The measure of each exterior angle is 30 degrees.
360
 30
n
360
 30
n
b) The measure of each interior angle is 135 degrees.
Bell Work
End
Quiz Practice
1) Find “x” and “y”.
2) Find each angle
A little more practice
• 3) Find a, b and c.
a
30
c
b
Exit Ticket
1. Name the polygon by the number of its sides.
Then tell whether the polygon is regular or
irregular, concave or convex.
1. Find the sum of the interior angle measures of a
convex 11-gon.
2. Find the measure of each interior angle of a
regular 18-gon.
3. Find the measure of each exterior angle of a
regular 15-gon