Please make a new notebook

It’s for Chapter 6/Unit 3Properties of

Quadrilaterals and Polygons

Then, would someone hand out papers, please? Thanks.♥

Chapter 6 Polygons and Quadrilaterals

to Unit 3

Properties of

Quadrilateral

s

Please get:•6 pieces of patty paper•protractor•Your pencil

But first

…

Let’s define ‘polygon’

The word ‘polygon’

is a Greek word.Poly means many and

gon means angles

What else do you know about a

polygon?

In this activity, we are going explore the interior and exterior angle measures of polygons.

Let’s define ‘polygon’

The word ‘polygon’

is a Greek word.Poly means many and

gon means angles

What else do you know about

a polygon?

♥A two dimensional object♥A closed figure♥Made up of three or more straight line segments♥There are exactly two endpoints that meet at a vertex♥The sides do not cross each other

There are also different types of polygons:

Convex polygons have interior angles less than 180◦

convex

concave

Concave polygons have at least one interior angle greater than 180◦

K1L1 M1

N1 O1 P1

Q1 R1 S1

Let’s practice:

•Decide if the figure is a polygon. •If so, tell if it’s convex or concave. •If it’s not, tell why not.

Ok, now where were

we?

and the interior and exterior

angle measures.

Oh, yes, an activity about

polygons...

1.

Draw a large scalene acute triangle on a piece of patty paper.Label the angles INSIDE the triangle as a, b, and c.

2.

On another piece of PP, draw a line with your straightedge and put a point toward the middle of the line.

Place the point over the vertex of angle a and line up one of the rays of the angle with the line. 3

.

4.

Trace angle a onto the second patty paper.

5.

Trace angles b and c so that angle b shares one side with angle a and the other side with angle c.

Should look like this:

What did you

just prove about

the interior angle

measures of a

triangle?

Yep. They equal 180◦

1.

2.

3.

4.

5.

Draw a quadrilateral on another PP. Label the angles a, b , c, and d.

Draw a point near the center of a second PP and fold a line through the point.

Place the point over the vertex of angle a and line up one of the rays on the angle with the line. Trace angle a onto the second PP.

Trace angle b onto the second PP so that a and b are sharing the vertex and a side

Repeat with angles c and d.

What did you

just prove about

the interior angle

measures of a

quadrilateral?

Yep. They equal 360◦

Tres mas…

1.

2.

Repeat these steps for a pentagon.Remember to figure the sum of the interior angles.

Repeat these steps for a hexagon.Remember to figure the sum of the interior angles.

Number of sides of the polygon

3 4 5 6 7 8

Sum of the interior angle measures

Can you find the pattern?Can you

create an

equation for the pattern?Put this table in your notes and complete it:

180 360 540 720 900 1080

Behold…

total sum of the interior

angles of a polygon

(The number of sides

of a polygon – 2)(180)

(n – 2)(180)

=

Or, as we mathematicians prefer to say…

QuadrilateralPentagon

180o 180

o180o

180o

180o

2 x 180o = 360o 3

4 sides5 sides

3 x 180o = 540o

Hexagon6 sides

180o

180o

180o

180o

4 x 180o = 720o

4 Heptagon/Septagon7 sides

180o180o 180o

180o

180o

5 x 180o = 900o 5

2 1 diagonal

2 diagonals

3 diagonals 4 diagonals Polygons

3.

♥On your PP with the triangle, extend each angle out to include the exterior angle.

♥Measure and record each linear pair.

♥What is the total sum of the exterior angles?

♥Do the same with the quadrilateral, pentagon and hexagon.

♥Remember to record each linear pair.

♥Can you make a conjecture as to the sum of exterior angles?Number of sides of the polygon

3 4 5 6 7 8

Sum of the interior angle measures

180 360 540 720 900 1080

Sum of the exterior angle measures 360 360 360 360 360 360

TADA!You have just proven two very important theorems:

Polygon Angle-Sum

Theorem (n-2) 180

Polygon Exterior

Angle-Sum TheoremAlways = 360◦

A quick polygon naming lesson:# of sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon/Septagon

8 Octagon

9 Nonagon

10 Decagon

12 Dodecagon

n n-gon

I ♥ Julius and Augustus

A regular polygon is equilateraland equiangular

TriangleSquare

Heptagon Octagon Nonagon

Pentagon Hexagon

Dodecagon

Let’s practice:

1. How would you find the total interior angle sum in a convex polygon?

2. How would you find the total exterior angle sum in a convex polygon?

3. What is the sum of the interior angle measures of an 11-gon?

4. What is the sum of the measure of the exterior angles of a 15-gon?

5. Find the measure of an interior angle and an exterior angle of a hexa-dexa-super-double-triple-gon.

6. Find the measure of an exterior angle of a pentagon.

7. The sum of the interior angle measures of a polygon with n sides is 2880. Find n.

(n-2)(180)

The total exterior angle sum is always 360◦

1620◦

360◦

180◦

360/5 = 72 ◦

2880 = (n-2)(180)n = 18 sides

Assignment

pg 3567 – 27,29-3540-41,49-54