1. ANGLES OF POLYGONS

2. Polygons  Definition: A polygon is a closed plane figure with 3 or more sides. (show examples)  Diagonal  Segment that connects two non-consecutive vertices

3. Kinds of Polygons  Convex –  no diagonal with points outside the polygon  Concave –  at least one diagonal with points outside the polygon  Equilateral  Equiangular  Regular –  all sides and angles are congruent; both equilateral and equiangular

4. Classification of Polygons (by number of sides)  Triangle –  Quadrilateral –  Pentagon –  Hexagon –  Heptagon –  Octagon –  Nonagon –  Decagon –  n – gon –

5. Naming Polygons  You can start anywhere on the polygon  Name the vertices in order  Example:

6. Angles of Polygons  Interior Angles –  Exterior Angles –

7. Sum of the Measures of the Interior Angles of a Polygon  (n-2)180  Where n=number of sides  This is true for ALL convex polygons!!!

8. Sums of Interior Angles  Triangle –  Rectangle –  Square –  Pentagon –  Hexagon –  Heptagon –  Octagon –  Nonagon –  Decagon –  n – gon – 180 360 540 720 900 1080 1260 1440 (n-2)180

9. Example: find the measure of angle D  First find the sum of the interior angles  Then find the measure of angle D  m<D= 132°

10. Exploring Polygons  If we have a regular triangle, what do we know about the interior and exterior angles and sides of this triangle?  They are congruent  If we have a regular rectangle, what do we know about this shape?  The sides are congruent. The interior and exterior angles are congruent. (square)

11. Exploring Polygons  If we have a regular pentagon, what do we know about the interior and exterior angles of this polygon?  If we have a regular hexagon, what do we know about:  Each interior angle  Each exterior angle

12. Measure of Each Interior Angle of a Regular Polygon  (n-2)180/n  Where n=number of sides  This is only true for REGULAR polygons!!!  What is the measure of each interior angle of a regular octagon?  (8-2)180/8= 135°

13. Sum of the measure of the exterior angles of a triangle  Triangle

14. Sum of the measure of the exterior angles of a quadrilateral  Quadrilateral

15. Sum of the measure of the exterior angles of a polygon  The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°.  This is true for ANY convex polygon!!!  The measure of each exterior angle in a regular polygon is  360 /n

16. Class work  p.356-357 #1-25 all, 29

17. Homework  3-5 worksheet