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CHAPTER

5

Learning about and

Demonstrating Polygon

Homes

The mathematicians may well jerk their minds

in a friendly and interested manner—I nonetheless am a

tinkerer to them. As well as the " artistic” ones will be primarily

inflammed. Still, might be I'm on the right track if I experience more delight from my own, personal little images than from the most beautiful

camera in the world... ”

Still Existence and Street, M. C. Escher, 1967–1968

©2002 Lien Art B. V. –Baarn–Holland.

All privileges reserved.

CHAPTER 5

TARGETS

в—Џ

Uncover the sum of

both the room and the

outdoor angle actions

in a polygon

в—Џ

Explore angle actions

of equiangular and legend

polygons

в—Џ

Discover properties

of kites, trapezoids,

and various kinds of

parallelograms

в—Џ

Define and discover

homes of midsegments in triangles

and trapezoids

в—Џ

Practice writing

flowchart and passage

proofs

в—Џ

Review graphing and

writing linear equations

в—Џ

Master new language

в—Џ

Practice construction

skills

в—Џ

Develop reasoning,

problem-solving skills,

and cooperative habit

OBJECTIVES

With this chapter you can expect to

в—Џ examine properties of convex

polygons

в—Џ discover relationships

among all of their angles, attributes,

and diagonals

в—Џ understand real-world

applications of special

polygons

The woodcut by M. C. Escher shows many

different polygons and near-polygons, as well as

polygons changing form as they recede into the

history. [Ask] " What polygons do you discover? ”

[rectangles (books, windows), squares (windows),

triangles (fence on the top ), parallelograms (tops

of books noticed in perspective), trapezoids (sides of

buildings diminishing into background)]

PART 5 Finding and Showing Polygon Homes

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LESSON

5. you

PLANNING

LESSON OUTLINE

Polygon Sum Conjecture

LES T ON

five. 1

There are many kinds of triangles, but

My spouse and i find that the harder I work,

a lot more luck We seem to have.

THOMAS JEFFERSON

One day:

15 min Exploration

10 min Sharing

in Chapter four, you discovered that the

sum of their angle measures is actually

180В°. In this lesson you are going to investigate

the sum from the angle measures in

convex quadrilaterals,

pentagons, and other

polygons. Then

you are going to look for a

design in the total

of the perspective measures

in any polygon.

a few min Shutting

15 min Exercises

Research

MATERIALS

Do they offer a Polygon Quantity Formula?

в…·

construction tools

в…·

protractors

You will need

в…·

calculators

в—Џ

в…·

Window Frame (T) for starters Step

в…·

Quadrilateral Amount Conjecture (W),

optional

в…·

Sketchpad activity Polygon Sum

Conjecture, optionally available

TEACHING

College students find that most polygons

together with the same range of sides

have a similar angle assess

sum. Conversely, knowing this kind of

sum permits students to find the

number of factors.

Draw the polygon. Properly measure all the interior perspectives, then locate the quantity.

Step 2

Discuss your benefits with your group. If you scored carefully, you must all have similar sum! In case your answers usually are exactly the same, locate the average.

3

Copy the table below. Repeat Actions 1 and 2 with different polygons, or share benefits with other organizations. Complete the table.

Quantity of sides of polygon

a few

Sum of measures of angles

180В°

Quadrilateral Quantity Conjecture

four

5

six

7

eight

360В° 540В° 720В° 900В° 1080В°

…

n

…

180В°(n ПЄ 2)

C-29

?. 360В°

The sum in the measures from the four room angles of any dihedral is бЋЏ

Pentagon Sum Conjecture

Guiding the Exploration

258

The first step

You can now produce some hypothese.

[ELL] You could review the terms

cuboid, pentagon, hexagon,

heptagon, and octagon.

1 Step

Show the Window Frame transparency and pose this problem:

" You need to build a window

body for an octagonal windowpane

like this one. To make the frame,

you are going to...