Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
3.4 The Polygon Angle-Sum Theorems Chapter 3: Parallel and Perpendicular Lines 3.4 The Polygon Angle-Sum Theorems Polygon: a closed plane figure with at least three sides that are segments A polygon Not a polygon; Not enclosed Not a polygon; Two sides intersect Naming a Polygon Name a polygon by its vertices. A ABCDE or AEDCB B E C D Start at one vertex and go around in order Naming a Polygon Three polygons are pictured. Name each polygon: L P M O N Classifying a Polygon by the number of sides: Sides 3 4 5 6 7 8 9 10 12 n Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon Convex vs. Concave A Convex Polygon has all vertices pointing “out” A Concave Polygon has one or more vertices “caving in” Classify Classify each polygon by its sides. Identify each as convex or concave: Hexagon; Convex Octagon; Concave Sum of Polygon Angle Measures Use triangles to figure out the sum of the angles in each polygon: # of Sides: # of Triangles: Total Degrees: # of Sides: # of Triangles: Total Degrees: Sum of Polygon Angle Measures Number of Sides 3 4 5 6 n Number of Triangles 1 Total Degrees inside Polygon 180 Theorem 3-9 Polygon Angle Sum Theorem The sum of the measures of the angles in a polygon is (n – 2)180. Find the sum of the measure of the angles of a 15-gon. Polygon Angle Sum The sum of the measures of the angles of a given polygon is 720. How many sides does the polygon have? Use (n – 2)180 : Using Polygon Angle-Sum Theorem Find the measure of <Y in pentagon TVYMR at the right. R 135° M T Use (n – 2)180 90° Y V Write an equation to solve for <Y Using Polygon Angle-Sum Theorem Pentagon ABCDE has 5 congruent angles. Find the measure of each angle. Use the Polygon Angle-Sum Theorem: (n – 2)180 Divide the total number of degrees by the number of angles: Exterior Angles What do you notice about each set of exterior angles? 80° 75° 115° 2 1 150° 99° 130° 71° 70° 86° 88° 1: 3 2: 70° 46° 3: Theorem 3-10 Polygon AngleSum Theorem The sum of one set of exterior angles for any polygon is 360°. 1 5 2 4 3 m<1 + m<2 + m<3 + m<4 + m<5 = 360° Polygons Equilateral Polygon: all sides congruent Equiangular Polygon: all angles congruent Regular Polygon: all sides and all angles congruent (equiangular and equilateral) *If a polygon is a regular polygon then all of the exterior angles are also congruent. Homework Pg 147 1-25, 40-44, 47-49