A polygon is a simple, closed figure in a plane formed by three or more straight sides that meet only at their endpoints or vertices. Common polygons include triangles with 3 sides, quadrilaterals with 4 sides, pentagons with 5 sides, and hexagons with 6 sides. Less common polygons have 7, 9, or 12 sides. A diagonal joins two non-consecutive vertices. A regular polygon has all sides of equal length and all interior angles of equal measure. The sum of the interior angles of any polygon with n sides is (n-2)×180 degrees.

1. Basic Geometry Unit 10.6 – Polygons

2. Polygons A polygon is a simple, closed figure in a plane that is formed by three or more sides . The sides meet only at the vertices .

3. Frequently Used Types of Polygons: Triangle 3 sides Quadrilateral 4 sides Pentagon 5 sides Hexagon 6 sides Octagon 8 sides Decagon 10 sides

4. Less Frequently Used Polygons 7 sides – Heptagon 9 sides – Nonagon 12 sides - Dodecagon

5. Diagonals & Regular Polygons A diagonal is a line segment that joins two nonconsecutive vertices. A regular polygon is a polygon that is equilateral (all sides congruent) and equiangular (all angles congruent.)

6. Sums of Interior Angles of Polygons If a polygon has n sides, then n - 2 triangles are formed, and the sum of the degree measures of the interior angles of the polygon is ( n - 2) 180. Shape Sides Angle Sum Triangle Quad- rilateral Pentagon Hexagon “ n” - gon

7. A dodecagon is a polygon with 12 sides. Find the sum of the measures of the angles of a dodecagon by using the formula. A stop sign is an octagon. For your model railroad village, you use miniature stop signs. What is the measure of each angle of the stop sign?

8. Questions? Homework 10.6 pg 529 #4-49