1. 6.1 Polygons

2. Targets: Identify, name, and describe polygons.
Find and Use the sum of the measures of the interior angles of a polygon.
Find and Use the sum of the measures of the exterior angles of a polygon.

3. Definitions:
SIDE
Polygon—a plane figure that meets the following conditions:
It is formed by 3 or more segments called sides, such that no two sides with a common endpoint are collinear.
Each side intersects exactly two other sides, one at each endpoint.
Vertex – each endpoint of a side. Plural is vertices. You can name a polygon by listing its vertices consecutively. For instance, PQRST and QPTSR are two correct names for the polygon above.

4. Example 1: Identifying Polygons
State whether the figure is a polygon. If it is not, explain why.
Not D – has a side that isn’t a segment – it’s an arc.
Not E– because two of the sides intersect only one other side.
Not F because some of its sides intersect more than two sides/
Figures A, B, and C are polygons.

5. Polygons are named by the number of sides they have – MEMORIZE
Type of Polygon 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon

6. Polygons are named by the number of sides they have – MEMORIZE
Type of Polygon 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon n
n-gon

7. Convex or concave?
Convex if no line that contains a side of the polygon contains a point in the interior of the polygon.
Concave or non-convex if a line does contain a side of the polygon containing a point on the interior of the polygon.
See how it doesn’t go on the
Inside-- convex
See how this crosses
a point on the inside?
Concave.

8. Convex or concave? CONCAVE CONVEX
Identify the polygon and state whether it is convex or concave.
CONCAVE
A polygon is EQUILATERAL
If all of its sides are congruent.
A polygon is EQUIANGULAR
if all of its interior angles are congruent.
A polygon is REGULAR if it is
equilateral and equiangular.
CONVEX

9. Identifying Regular Polygons
Heptagon is equilateral, but not equiangular, so it is NOT a regular polygon.
Remember: Equiangular & equilateral
Decide whether the following polygons are regular.
Pentagon is equilateral and equiangular, so it is a regular polygon.
Equilateral, but not equiangular, so it is NOT a regular polygon.

10. Angles of Polygon Laws
Sum of the Interior angles of a convex Polygon = (n - 2) 180, where n = # of sides of the polygon
Sum of the Exterior angles of a convex polygon = 360.
One interior angle of a regular polygon = [(n-2) 180] / n, where n = # of sides