This document defines and provides examples of polygons, congruent polygons, and similar polygons. It begins by defining a polygon as a plane figure with three or more sides, and notes there are different types including convex, concave, and regular polygons. It then defines congruent polygons as having the same size and shape, and similar polygons as having the same shape but different sizes, with corresponding angles and sides that are proportional. Examples are provided to illustrate finding side lengths of similar polygons using size-change factors.

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

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

6. 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 . . .

8. Can you find the similar
matches?

9. 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

10. Now, let’s define similar !!
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:

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 is1X 2X 1
2
x

12. 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.

13. 1.5 cm
2 cm
3 cm
T
C
(1) Each side in the larger triangle is twice the size of
the corresponding side in the smaller triangle.
A
G
D
O
3 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

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

15. Example 1: Quadrangles ABCD and EFGH are similar.
How long is side AD? How long is side GH?
15 cm
? cm
18 cm
12cm
7cm
6cm
4cm
?cm
B
C
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

16. Example 2 : Figure MORE is similar to Figure SALT.
Select the right answer with the one of
the given values below.
(1) The length of segment TL.
a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cm
(2) ER corresponds to this segment.
a. TS b. TL c. AL d. SA
(3) EM corresponds to this segment.
a. TS b. TL c. SA d. AL
(4) The length of segment MO.
a. 6 cm b. 6.5 cm c. 7 cm d. 7.5 cm
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17. 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