What is a polygon?

What are the different types of polygons?

What is a congruent polygon?

What is a similar polygon?

What are some examples of these polygons?

A polygon is a plane having three or more sides.

Convex polygon: all the sides are pushed outward.Concave polygon: at least two sides are pushed inward.Regular polygon: all the sides have the same length and their angles are all the same size.

Take a minute to match the name up with the figure . . .

Congruent polygons are polygons that have the same size and the

same shape.

fact:

fact: Congruent shapes have all their sides and angles congruent.

Notice how the second figures have the same shape

and size of the first – they match exactly.

Now we are going to take a look at similar polygons . . .

Can you find similar polygons?

(1) Triangle

(2) Rectangle

(3) Pentagon

(4) Hexagon

(5) Octagon

Same shape

Different size

Angle does not change

Enlargement

Reduction

Definition: Figures that have exactly same shape are called similar figures.

(1) In polygons, the size of angles does not change.

(2) One figure is an enlargement or reduction of the other.

(3) Congruent figures are similar because they gave the same shape.

Properties:

How can we know the length of sides in similar figures?

If two figures are similar, one figure is an enlargement of the other. The size-change factor tells the amount of enlargement or reduction.

Example 1: If a copy machine is used to copy a drawing or picture, the copy will be similar to the original.

Original Copy

Exact Copy

Copy machine set to 100%

Size-change factor is

Original Copy

Enlargement

Copy machine is set to 200%

Size-change factor is

Original Copy

Reduction

Copy machine is set to 50%

Size-change factor is1X 2X

1

2x

Example 2: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO?

C

A

T G

O

D

1.5 cm

3 cm

2 cm

3 cm

6 cm

? cm

Each side and its enlargement form a pair of sides called corresponding sides.

(1) Corresponding side of TC --> GD

(2) Corresponding side of CA--> DO

(3) Corresponding side of TA--> GO

Length of

corresponding sides

GD=3

TC=1.5

DO=6

CA=3

GO=?

TA=2

Ratio of Lengths 3/1.5=2 6/3=2 ?/2=2

The size-change factor is 2x.

(1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle.

1.5 cm

2 cm

3 cm

T

C

A

G

D

O3 cm

6 cm

? cm

(2) Now, let’s find the length of side GO

i) What side is corresponding side of GO? TA

ii) What is the size-change factor? 2X

iii) Therefore, GO= size-change factor x TA

iv) So, GO= 2 x 2 = 4 cm

Same shapeDifferent size

Corresponding side Size-change factor

Not change angle

Similar polygons

Example 1: Quadrangles ABCD and EFGH are similar. How long is side AD? How long is side GH?

15 cm

? cm

18 cm

12cm7cm

6cm

4cm

?cm

BC

A

D

H

E

GF

(1) What is size-change factor?

(2) What is corresponding side of AD ?

(3) How long is side AD?

(4) What is corresponding side of GH?

(5) How long is side GH?

12÷ 4= 3 & 18÷ 6=3

EH

AD = 5

CD

7 x 3 = GH, GH = 21

A polygon is a plane having three or more sides.

Congruent polygons are polygons that have the same size and the same shape.

Similar polygons are polygons that have the same shape.

congruent congruent

similar similar

Circle Limit IIICircle Limit IIIM.C. EscherM.C. Escher

Similar figures look alike but one is a smallerSimilar figures look alike but one is a smaller version of the other. Like Dr. Evil and Mini-Me.version of the other. Like Dr. Evil and Mini-Me. It wouldn’t make much sense to make a drawing It wouldn’t make much sense to make a drawing of this ship the actual size of the ship. of this ship the actual size of the ship.

Just like congruent polygons, the correspondingangles in similar polygons must be congruent.

AA XX

CCDD

BB WW

ZZ YY

A = 80° B = 30° Z = 170°A = 80° B = 30° Z = 170°

W = ___ X = ___ D = ___W = ___ X = ___ D = ___80°80° 30° 170°170°

The sides are a little different.The sides are a little different.

They must be They must be PROPORTIONAL.PROPORTIONAL.

AA XX

CCDD

BB WW

ZZ YY

ABAB = = BCBC = = CDCD = = DADA

WX XYWX XY YZ ZWYZ ZW

This means I should be able to multiply each sideThis means I should be able to multiply each sideof the smaller polygon by the same number andof the smaller polygon by the same number andget it’s corresponding side on the bigger polygon.get it’s corresponding side on the bigger polygon.

444x2 = 84x2 = 8

555x2 = 105x2 = 10

222x2 = 42x2 = 4

333x2 = 63x2 = 6

The The SCALE FACTORSCALE FACTOR is the ratio is the ratio of the corresponding sidesof the corresponding sides

SMALLSMALL BIGBIG BIG SMALLBIG SMALL

oror

What is the scale factor of these polygons?What is the scale factor of these polygons?

1010

44

XX 77

YY88

ZZ66

Scale FactorScale Factor = = 101044

== 5522

44

77

YY

ZZ

1010

XX

88

66

101044

== 5522

Use the scale factor to find the other sidesUse the scale factor to find the other sides

55 662 Z2 Z==

5z = 125z = 12 z = z = 1212 = 2.4 = 2.4 55

SF =SF =

55 XX2 72 7

2x = 352x = 35 x = x = 35 35 = 17.5= 17.5 22

== 55 882 Y2 Y

5y = 165y = 16 y = y = 1616 = 3.2 = 3.2 55

==