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In this chapter you will ● study properties of convex polygons

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

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In this chapter you will ● study properties of convex polygons

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  1. 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

  2. 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

  3. 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

  4. JRLeon Discovering Geometry Chapter 5.1 HGSH

  5. 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

  6. Example 1: Use the Polygon Sum Conjecture to complete the table. 180°(n-2) JRLeon Discovering Geometry Chapter 5.1 HGSH

  7. 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

  8. Polygon - Sum of exterior angles JRLeon Discovering Geometry Chapter 5.2 HGSH

  9. Polygon - Sum of exterior angles JRLeon Discovering Geometry Chapter 5.2 HGSH

  10. JRLeon Discovering Geometry Chapter 5.2 HGSH

  11. 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

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