University:
Missouri State University
Course:
MTH 460 | College Geometry
Academic year:

2021
Views:

240

Pages:

7
Author:

Kolten Khan

Today's objectives: 1. Recognize and name convex polygons and regular polygons. 2. Find the measures of interior and exterior angles of convex polygons. Geometry/Trigonometry II 3.5 Angles of a Polygon Name New Terminology Polygon A plane figure formed by coplanar segments such that: + 1. Each seg. intersects exactly two other seg.'s, one at each endpoint 2. No two segments with a common endpoint are collinear How many sides does es a have? A polygon E 4 sides Examples of polygons: Examples that are not polygons: Convex Polygon- a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. Examples of convex polygons: nonconvex: Place the name of the polygon next to the number of sides it has. 3. Triangle 4- Quadrilateral 5. Pentagon 6- Hexagon 7- Heptagon 8. Octagon 9- Nonagon 10- Decagon -n-gon 12-dodecagon 15 sides 15-gon 23 sides 23-gon. Terms used for triangles like vertices, angles, and sides are also used for polygons. A polygon's vertices are labeled in consecutive order just like that of a plane's. Diagonal-Segment joining two nonconsecutive vertices A B B 1 1 A C 2C 2 F4 3 3 E D Every Penteson has 3 A's inside it Int. Angle Sum = 3(180)=540° Every Hexaçon has 4 As mside of it. Int. Angle Sum = 4(180) = 120° Theorem 3-13 The sum of the measures of the angles of a convex polygon with n sides is (n - 2) * 180 78 108 16872 108 n ^ i 120 10120 1260 120 120 60 90 90 n = 4 n=5 Int. chi*Sum = (4 - 2)(100) (5 - 2)(150) = (2Xwo) (3)(180) (6 - 2)(188) (4)(180) =360 =540 Ext. 4. Sum = 4(80 +180 =5(72) =6(66) = 360 deg = 720 deg n = psi = 360 deg \mathfrak{V} 90 deg = 360 deg plus/minus 180