What does the word “polygon” What does the word “polygon” mean?mean?

What is the smallest number What is the smallest number of sides a polygon can have?of sides a polygon can have?

What is the largest number of What is the largest number of sides a polygon can have?sides a polygon can have?

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

n-gon

Polygons with 3 sides… TrianglesPolygons with 4 sides… Quadrilaterals

Polygons with 5 sides.. PentagonsBut wait we have more polygons

Polygons with 6 sides… HexagonsPolygons with 7 sides… HeptagonsPolygons with 8 sides… OctagonsBut still we have more polygons

Polygons with 9 sides… NonagonsPolygons with 10 sides… Decagons

Polygons with 12 sides… DodecagonsAnd now we have our polygons

Hip Bone’s connected to the…Classifying Polygons

F

A B

C

DE

Important TermsA VERTEX is the point of intersection of two sides

A segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL.

CONSECUTIVE VERTICES are two endpoints of any side.

Sides that share a vertex are called CONSECUTIVE SIDES.

More Important Terms

EQUILATERAL - All sides are congruentEQUIANGULAR - All angles are congruentREGULAR - All sides and angles are congruent

Polygons are named by listing its vertices consecutively.

A B

E D

CF

Polygons can be CONCAVE or CONVEX

CONVEX

CONCAVE

Ex. 3 Classify each polygon as convex or concave.

What is the sum of the measures of the interior angles of a triangle?

180°180°

What is the sum of the measures of the interior angles of any

quadrilateral?

REVIEW:REVIEW:

180°

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 n-2 (n-2) 180

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.

B)Find the measure of ONE interior angle

540°

108°

Two more important terms

Exterior Angles

Interior Angles

If any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

2

3

4

5

m m m m m 1 2 3 4 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 m m 1 2 3 360

If any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

3

2

4

m m m m 1 2 3 4 360

Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.

60°

sum of the exterior anglesnumber of sides

3606

Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?

n = 20

angleexterior sides ofnumber

anglesexterior theof sum

18360

n

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