Section 3-5 Angles of Polygons

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Objectives Classify polygons based on their sides and angles.

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Presentation transcript:

Section 3-5 Angles of Polygons Objective: Recognize and name the convex polygons and regular polygons. Find the measures of the interior angles and exterior angles of convex polygons. Standard 2.9 Concepts in Geometry

The left five figures are polygons. The right figures are not The left five figures are polygons. The right figures are not. Using this knowledge, write the definitions or qualities a polygon can/cannot have.

Polygons Made up of segments (thus no curves) Must have three or more sides Can be non-convex but we focus on convex. Ex. Non-Convex where there is at least one line that is interior

Convex vs. Non-Convex

Naming Polygons Number of Sides Name 3 Triangle 4 Quadrilateral 5 6 8 10 n Name Triangle Quadrilateral Pentagon Hexagon Octagon Decagon n-gon

How many different triangles can be forms by drawing diagonals through the following polygons Definition of diagonal: interior segment from one vertex to another. 4 sides & 2 triangles 6 sides & 4 triangles 3 sides & 1 triangles 8 sides & 6 triangles

Investigation-Fill in the chart and make a conjecture: #of sides #of angle sum 3 4 5 6 7 8 9 10 15 20 n

Theorem 3-13 The sum of the measures of the angles of a convex polygon with n sides is (n-2) 180 Interior Angle Thm

Exterior Angle Sum Theorem Theorem 3-14 The sum of the measures of the exterior angles of any convex polygon, one angle at each, is 360 Exterior Angle Sum Theorem

Ex. If a polygon has 22 sides. Find the interior and exterior angle sum. Interior sum (n-2) 180 (22-2) 180 (20) 180 3600 Exterior sum 360

Regular Polygons Regular polygons are equiangular and equilateral. Thus all their interior angles are ______ and all their sides are _______.

Example 1 All regular 7 sided figures have interior angle measures of ____ and exterior angle measures of _____. Answers: int = 128.5 ext = 51.5

Example 2 All regular 6 sided figures have interior angle measures of ____ and exterior angle measures of _____. Answers: int = 120° and ext = 60°.

Group Work CE p. 103 #1-6 and 9 HW WE p.104 #1-23 all