Unit 2

Polygons

In The Plane

These figures are not polygons These figures are polygons

Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.

Polygons

Classifications of a Polygon

Convex: No line containing a side of the polygon contains a point in its interior

Concave:

A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.

Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length

Irregular: Two sides (or two interior angles) are not congruent.

Classifications of a Polygon

Polygon Names

3 sides Triangle

4 sides

5 sides

6 sides

7 sides

8 sides

Nonagon

Octagon

Heptagon

Hexagon

Pentagon

Quadrilateral

10 sides

9 sides

12 sides

Decagon

Dodecagonn sides n-gon

Convex Polygon Formulas…..

2 180n

n

2 180n

360

Diagonals of a Polygon:

For a convex polygon with n sides:

The sum of the interior angles is

A segment connecting nonconsecutive vertices of a polygon

The measure of one interior angle is

The sum of the exterior angles is

The measure of one exterior angle is 360

n

Examples…..

360 36045

8n

2 180 (30 2) 180 28 180168

30 30

n

n

1. Sum of the measures of the interior angles of a 11-gon is

(n – 2)180° (11 – 2)180 ° 1620

2. The measure of an exterior angle of a regular octagon is

3. The number of sides of regular polygon with exterior angle 72 ° is

4. The measure of an interior angle of a regular polygon with 30 sides

360 3605

72n n

exterior angle

The End!