1. Lesson 1-6
Polygons
Lesson 3-4: Polygons

2. 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 are not polygons
These figures are polygons
Lesson 3-4: Polygons

3. 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

4. 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

5. What is this shape?
Lesson 3-4: Polygons

6. What is this shape?
Lesson 3-4: Polygons

7. What is this shape?
Lesson 3-4: Polygons

8. What is this shape?
Lesson 3-4: Polygons

9. What is the shape?
Lesson 3-4: Polygons

10. Polygon Names 3 sides Triangle 4 sides Quadrilateral 5 sides Pentagon
Hexagon
7 sides
Heptagon
8 sides
Octagon
9 sides
Nonagon
10 sides
Decagon
Dodecagon
12 sides
n sides
n-gon
Lesson 3-4: Polygons

11. Perimeter: Given P=144, find the value of x and the length of each side.
Lesson 3-4: Polygons

12. 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

13. Examples….. Sum of the measures of the interior angles of a 11-gon is
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