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What does the word “polygon” mean?
What is the smallest number of
sides a polygon can have?
What is the largest number of
sides a polygon can have?
Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Hexagon
Dodecagon
Heptagon
n-gon
Hip Bone’s connected to the…
Classifying Polygons
Polygons with 3 sides… Triangles
Polygons with 4 sides… Quadrilaterals
Polygons with 5 sides.. Pentagons
But wait we have more polygons
Polygons with 6 sides… Hexagons
Polygons with 7 sides… Heptagons
Polygons with 8 sides… Octagons
But still we have more polygons
Polygons with 9 sides… Nonagons
Polygons with 10 sides… Decagons
Polygons with 12 sides… Dodecagons
And now we have our polygons
Important Terms
A VERTEX is
the point of
intersection of
two sides
A
B
F
A segment whose
endpoints are two
nonconsecutive
vertices is called
a DIAGONAL.
CONSECUTIVE
VERTICES are two
endpoints of any side.
C
E
D
Sides that share a vertex are called
CONSECUTIVE SIDES.
More Important Terms
EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent
Polygons are named by listing its
vertices consecutively.
A
B
C
F
E
D
Polygons can be CONCAVE or CONVEX
CONCAVE
CONVEX
Ex. 3 Classify each polygon as convex or concave.
REVIEW:
What is the sum of the measures of the
interior angles of a triangle?
180°
180°
180°
What is the sum of the measures of the
interior angles of any quadrilateral?
360°
# of
sides
# of
triangles
Sum of
measures of
interior angles
3
1
1(180) = 180
4
2
2(180) = 360
5
3
3(180) = 540
6
4
4(180) = 720
n-2
(n-2) 180
n
If a convex polygon has n sides,
then the sum of the measure of the
interior angles is
(n – 2)(180°)
Ex. 1 Use the regular pentagon to
answer the questions.
A)Find the sum of the
measures of the interior
angles.
540°
B)Find the measure of
ONE interior angle
108°
Two more important terms
Interior
Angles
Exterior
Angles
If any convex
polygon, the sum of
the measures of the
exterior angles, one at
each vertex, is 360°.
2
1
3
5
4

m1  m2  m3  m4  m5  360
If any convex
polygon, the sum of
the measures of the
exterior angles, one at
each vertex, is 360°.
1
3
2

m1  m2  m3  360
If any convex
polygon, the sum of
the measures of the
exterior angles, one at
each vertex, is 360°.
1
2
4
3

m1  m2  m3  m4  360
Ex. 2 Find the measure of ONE exterior
angle of a regular hexagon.
sum of the exterior angles

number of sides

360

6
60°
Ex. 3 Find the measure of ONE
exterior angle of a regular heptagon.
sum of the exterior angles

number of sides

360

7
51.4°
Ex. 4 Each exterior angle of a polygon
is 18. How many sides does it have?
sum of the exterior angles
 exterior angle
number of sides

360
 18
n
n = 20
Ex. 5 The sum of the measures of five interior
angles of a hexagon is 535. What is the measure
of the sixth angle?
185°
Ex. 6 The measure of the exterior angle of a
quadrilateral are x, 3x, 5x, and 3x. Find the
measure of each angle.
30°, 90°, 150°,
and 90°
Ex. 7 If each interior angle of a regular polygon is
150, then how many sides does the polygon have?
n = 12