1. Welcome
to the
Wonderful World of
Polygons

2. What We Hope You Learn by the End of this Presentation:
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?

3. A polygon is a plane having three or more sides.
What Is a Polygon?
A polygon is a plane having three or more sides.
Types of Polygons:
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.

4. Let's Play a Polygon Matching Game:
Take a minute to match the name up with the figure . . .
pentagon
triangle
octagon
quadrilateral
hexagon
heptagon

5. What are Congruent Polygons?
Congruent polygons are polygons that have the same size and the same shape.
fact:
Congruent shapes have all their sides and angles congruent.
fact:

6. Let's See Some Congruent Polygons:
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 . . .

7. What are Similar Polygons?
Let's find some examples outdoors.

8. Can you find the similar matches?
Now, Let's Think about Similar in Mathematics!!

9. Can you find similar polygons?
(1) Triangle
Same shape
(2) Rectangle
Different size
(3) Pentagon
Angle does not change
(4) Hexagon
Reduction
(5) Octagon
Enlargement

10. Now, let’s define similar !!
Definition:
Figures that have exactly same shape are called similar figures.
Properties:
(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.

11. 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 is 1X 2X

12. Example 2: The triangles CAT and DOG are similar
Example 2: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO? T G
2 cm
? cm
1.5 cm A
3 cm O C
3 cm
6 cm D
Each side and its enlargement form a pair of sides called corresponding sides.
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 GD
(1) Corresponding side of TC -->
(2) Corresponding side of CA--> DO
The size-change factor is
2x.
(3) Corresponding side of TA--> GO

13. (2) Now, let’s find the length of side GO
? cm T
2 cm
3 cm O
1.5 cm A
6 cm
3 cm C D
(1) Each side in the larger triangle is twice the size of the corresponding side in the smaller triangle.
(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

14. What we just learned about similar polygons ?
Not change angle
Different size
Same shape
Similar polygons
Corresponding side
Size-change factor

15. Now, you try... Example 1: Quadrangles ABCD and EFGH are similar.
How long is side AD? How long is side GH?
What is size-change factor?
What is corresponding side of AD ?
How long is side AD?
What is corresponding side of GH?
How long is side GH?
12÷ 4= 3 & 18÷ 6=3 EH
AD = 5 CD
7 x 3 = GH, GH = 21

16. Let's Go Over What We Just Learned:
What is a polygon?
A polygon is a plane having three or more sides.
What are congruent polygons?
congruent
congruent
Congruent polygons are polygons that have the same size and the same shape.
What are similar polygons?
similar
similar
Similar polygons are polygons that have the same shape.

17. Similar Polygons
Circle Limit III
M.C. Escher

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

19. Just like congruent polygons, the corresponding
angles in similar polygons must be congruent.

20. A = 80° B = 30° Z = 170° W = ___ X = ___ D = ___ B A W X Z Y D C 80°

21. AB = BC = CD = DA B A W X Z Y D C The sides are a little different.
They must be PROPORTIONAL.
AB = BC = CD = DA
WX XY YZ ZW B A W X Z Y D C

22. This means I should be able to multiply each side
of the smaller polygon by the same number and
get it’s corresponding side on the bigger polygon.
4x2 = 8 4
3x2 = 6
5x2 = 10 3 5 2
2x2 = 4

23. The SCALE FACTOR is the ratio of the corresponding sides
SMALL BIG
BIG SMALL

24. What is the scale factor of these polygons?10 4 6 X 7 Z Y 8 10 4 5 2 =
Scale Factor =

25. 10 4 = 5 2 Use the scale factor to find the other sides 5y = 167 Z 6 X 10 4 = 5 2 Y
SF = 8
2 Z =
5 X
2 Y = =
5y = 16
y = 16 = 3.2 5
5z = 12
z = 12 = 2.4 5
2x = 35
x = 35 = 17.5 2

26. The End!