 To Classify polygons  To find the sums of the measures of the interior and exterior angles of polygons.

 Polygon—a plane figure that meets the following conditions:  It is formed by 3 or more segments called sides, such that no two sides with a common endpoint are collinear.  Each side intersects exactly two other sides, one at each endpoint.  Vertex – each endpoint of a side. Plural is vertices. You can name a polygon by listing its vertices consecutively. For instance, PQRST and QPTSR are two correct names for the polygon above. SIDE

 State whether the figure is a polygon. If it is not, explain why.  Not D – has a side that isn’t a segment – it’s an arc.  Not E– because two of the sides intersect only one other side.  Not F because some of its sides intersect more than two sides/ Figures A, B, and C are polygons.

Number of sidesType of Polygon 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon

Number of sidesType of Polygon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon

 Convex if no line that contains a side of the polygon contains a point in the interior of the polygon.  Concave or non-convex if a line does contain a side of the polygon containing a point on the interior of the polygon. See how it doesn’t go on the Inside-- convex See how this crosses a point on the inside? Concave.

 Identify the polygon and state whether it is convex or concave. A polygon is EQUILATERAL If all of its sides are congruent. A polygon is EQUIANGULAR if all of its interior angles are congruent. A polygon is REGULAR if it is equilateral and equiangular.

x°+ 2x° + 70° + 80° = 360° 3x = 360 3x = 210 x = 70 Sum of the measures of int.  s of a quadrilateral is 360° Combine like terms Subtract 150 from each side. Divide each side by 3. 80° 70° 2x° x°x° Find m  Q and m  R. m  Q = x° = 70° m  R = 2x°= 140° ►So, m  Q = 70° and m  R = 140°

 Sketch polygons with 4, 5, 6, 7, and 8 sides  Divide Each Polygon into triangles by drawing all diagonals that are possible from one vertex  Multiply the number of triangles by 180 to find the sum of the measures of the angles of each polygon. 1) Look for a pattern. Describe any that you have found. 2) Write a rule for the sum of the measures of the angles of an n-gon

 The sum of the measures of the angles of an n-gon is (n-2)180  Ex: Find the sum of the measures of the angles of a 15-gon  Sum = (n-2)180  = (15-2)180  = 13*180 = 2340

 The sum of the interior angles of a polygon is How many sides does the polygon have?  Sum = (n-2)180  9180 = (n-2)180  51 = n-2  53 = n  The polygon has 53 sides.

 The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.  An equilateral polygon has all sides congruent  An equiangular polygon has all angles congruent  A regular polygon is both equilateral and equiangular.

 The measure of an exterior angle of a regular polygon is 36. Find the measure of an interior angle, and find the number of sides.  Exterior angles = 360  Since regular,  n*36 = 360  n = 10  Since exterior angle = 36, interior angle  = 144