JRLeon Discovering Geometry Chapter 5.1 HGSH

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

● 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

OBJECTIVES:

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 concavepolygons?

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 5.2 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

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 14Lesson 5.2: Pages 263 - 264, Problems 1 through 11