Chapter 2 Investigating Geometric Figures 2-2 POLYGONS Objective: Classify polygons; find the sum of the measures of the interior and exterior angles of polygons 1 POLYGON: A closed plane figure formed by three or more segments that intersect only at their endpoints. NO GAPS, NO CROSS OVERS Tell whether the figure is a polygon. 2 Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal. 3 You can name a polygon by the number of its sides. 4 A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex. 5 All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that has all angles and sides are congruent. If a polygon is not regular, it is called irregular. 6 Draw a concave pentagon. Draw a convex irregular heptagon. 7 5 2 3 180 540 108 6 3 4 180 720 120 7 4 5 180 900 128.5 8 5 6 180 1080 135 10 7 8 180 1440 144 12 9 10 180 1800 150 8 Theorem 2-3 Polygon Interior Angle-Sum Theorem The sum of the interior angle measures of a convex polygon with n sides is (n - 2) 180°. http://www.mathopenref.com/polygoninteriorangles.html 9 1. Find the sum of the interior angle measures of a... convex heptagon. regular 16­gon. 10 In a regular polygon with n sides the measure of one interior angle is (n - 2)180 n 11 2. What is each measure of the interior angle of a regular 18­gon? What is each interior angle of a dodecogon? 12 3. Find the measure of the missing angle of the quadrilateral. 91° 79° x 125° 13 In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°. 14 Exterior Angles 15 Theorem 2-4 Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360°. 16 4. Find the measure of each exterior angle of a regular 20­gon. NOTE: One exterior angle of a regular polygon with n sides = 360 n 17 5. Find the value of b in polygon FGHJKL. 18 6. Ann is making paper stars for party decorations. What is the measure of ∠1? 19 7. Find the measure of each interior angle of pentagon ABCDE. You will have to find the value of c. 20 8. The measure of an exterior angle of a regular polygon is 60°. Find the number of sides. 21 HW # 19 p. 79­80 # 1­4,10­17,19­26 Quiz on Thursday !!!! 22.