ANGLES OF POLYGONS

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

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

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

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

Angles of Polygons  Interior Angles –  Exterior Angles –

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!!!

Sums of Interior Angles  Triangle –  Rectangle –  Square –  Pentagon –  Hexagon –  Heptagon –  Octagon –  Nonagon –  Decagon –  n – gon – (n-2)180

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°

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)

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

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°

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

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

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

Class work  p #1-25 all, 29

Homework  3-5 worksheet