Transcript Document

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
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