OBJECTIVES Discover the sum of both the interior

OBJECTIVES: ● Discover the sum of both the interior and the exterior angle measures in a polygon ● Explore angle measures of equiangular and star polygons ● Discover properties of kites, trapezoids, and various kinds of parallelograms ● Define and discover properties of midsegments in triangles and trapezoids ● Practice writing flowchart and paragraph proofs ● Review graphing and writing linear equations ● Learn new vocabulary ● Practice construction skills ● Develop reasoning, problem-solving skills, and cooperative behavior In this chapter you will ● study properties of convex polygons ● discover relationships among their angles, sides, and diagonals ● learn about real-world applications of special polygons JRLeon Discovering Geometry Chapter 5. 1 HGSH

There are many kinds of triangles, but in Chapter 4, you discovered that the sum of their angle measures is always 180°. In this lesson you’ll investigate the sum of the angle measures in convex quadrilaterals, pentagons, and other polygons. Then you’ll look for a pattern in the sum of the angle measures in any polygon. JRLeon Discovering Geometry Chapter 5. 1 HGSH

For this investigation each person in your group should draw a different version of the same polygon. For example, if your group is investigating hexagons, try to think of different ways you could draw a hexagon. Polygon - Sum of interior angles JRLeon Discovering Geometry Chapter 5. 1 HGSH

JRLeon Discovering Geometry Chapter 5. 1 HGSH

Developing Proof As a group, write a proof of the Quadrilateral Sum Conjecture using the diagram below. Does the Polygon Sum Conjecture apply to concave polygons? Possible proof: q + d +u = 180° and e + a = v 180° by the Triangle Sum Conjecture. q + d + e + a + v + u = 360° by addition property of equality. Therefore, the sum of the measures of the angles of a quadrilateral is 360°. JRLeon Discovering Geometry Chapter 5. 1 HGSH

Example 1: Use the Polygon Sum Conjecture to complete the table. 180°(n-2) JRLeon Discovering Geometry Chapter 5. 1 HGSH

In Lesson 5. 1, you discovered a formula for the sum of the measures of the interior angles of any convex polygon , 180°(n-2). In this lesson you will discover a formula for the sum of the measures of the exterior angles of a convex polygon. JRLeon Discovering Geometry Chapter 5. 2 HGSH

Polygon - Sum of exterior angles JRLeon Discovering Geometry Chapter 5. 2 HGSH

JRLeon Discovering Geometry Chapter 5. 2 HGSH

Classwork / Homework: Lesson 5. 1: Pages 259 - 260, Problems 1 through 14 Lesson 5. 2: Pages 263 - 264, Problems 1 through 11 JRLeon Discovering Geometry Chapter 5. 2 HGSH