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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.

These figures arenot polygons

These figures are polygons

Lesson 3-4: 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.

Lesson 3-4: Polygons

Classifications of a 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.

Lesson 3-4: Polygons

Polygon Names

Triangle

3 sides

4 sides

Quadrilateral

5 sides

Pentagon

6 sides

Hexagon

7 sides

Heptagon

8 sides

Octagon

9 sides

Nonagon

10 sides

Decagon

Dodecagon

12 sides

n sides

n-gon

Lesson 3-4: Polygons

Convex Polygon Formulas…..

Diagonals of a Polygon:

A segment connecting nonconsecutive vertices of a polygon

For a convex polygon with n sides:

The sum of the interior angles is

The measure of one interior angle is

The sum of the exterior angles is

The measure of one exterior angle is

Lesson 3-4: Polygons

Examples…..

- Sum of the measures of the interior angles of a 11-gon is
- (n – 2)180° (11 – 2)180 ° 1620
- The measure of an exterior angle of a regular octagon is
- The number of sides of regular polygon with exterior angle 72 ° is
- The measure of an interior angle of a regular polygon with 30 sides

Lesson 3-4: Polygons

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