1. Geometry Honors T HE P OLYGON A NGLE -S UM T HEOREM

2. Vocabulary Polygon –a closed plane figure formed by three or more segments. Each segment intersects exactly 2 other segments, but only at their endpoints, & no two segments with a common endpoint are collinear.

3. Vocabulary Vertices of a Polygon –the endpoints of the sides. Diagonal of a Polygon –a segment that connects two nonconsecutive vertices.

4. Activity Complete the word search. Within the word search you will find the names of various polygons. They include the names of a: 3 sided polygon, 4 sided polygon, 5 sided polygon, 6 sided polygon, 7 sided polygon, 8 sided polygon, 9 sided polygon, 10 sided polygon, 12 sided polygon and 20 sided polygon.

5. Types of Polygons Triangle – a polygon with 3 sides. Quadrilateral – a polygon with 4 sides. Pentagon – a polygon with 5 sides. Hexagon – a polygon with 6 sides.

6. Types of Polygons Heptagon – a polygon with 7 sides. Octagon – a polygon with 8 sides. Nonagon – a polygon with 9 sides. Decagon – a polygon with 10 sides.

7. Types of Polygons Dodecagon – a polygon with 12 sides. Icosagon – a polygon with 20 sides.

8. Discovery Draw a ______ and then draw as many diagonals as you can from 1vertex. How many triangles were formed? Determine the sum of all interior angles. Pentagon Hexagon Heptagon Octagon Nonagon n-gon

9. Theorem Polygon Angle-Sum Theorem–the sum of the measures of the interior angles of an n-gon is (n-2)*180 Example: Determine the sum of the interior angles of an 18 sided figure.

10. Vocabulary Equilateral Polygon –a polygon with all sides congruent. Equiangular Polygon–a polygon with all angles congruent. Regular Polygon –a polygon that is both equilateral and equiangular.

11. Vocabulary Concave Polygon –a polygon that has at least one diagonal with points outside the polygon. Convex Polygon – a polygon with no diagonal with points outside the polygon.

12. Corollary Corollary to the Polygon Angle Sum Theorem–the measure of each interior angle of a regular n-gon is (n-2)*180 n Example: Determine the measure of each interior angle of a regular octagon.

13. Application Example: Determine the measure of the missing angle: 87  95  32  120  xx

14. Theorem Polygon Exterior Angle-Sum Theorem–the sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. Example: Find the measure of an exterior angle of a regular hexagon.

15. H OMEWORK Pg. 147: 1-25, 32-35, 40-44, 47-49.