Ratio of Similitude

Ratio of Similitude

The ratio of similitude of two similar polygons is the ratio of the lengths of any two corresponding sides.

C’

B’A’

C

BA

2410

6

20 12

12

1

2

6

12

''

BA

AB

1

2

10

20

''

CB

BC

1

2

12

24

''

AC

CA

It doesn’t matter the sides, they have the same ratio!

Other segments that have the same ratio as the sides:

Page 36

Lets look at the perimeters…

C’

B’A’

C

BA

2410

6

20 12

12

Remember: perimeter is the sum of all sides!

CABCABP ABC

242012 ABCP

56ABCP

''''''''' ACCBBAP CBA

12106''' CBAP

28''' CBAPRemember:

1

2

6

12

''

BA

AB 1

2

28

56

'''

CBA

ABC

P

PRatio of perimeters = ratio of the sides

Page 36

Page 37

𝟑𝟎𝒙

31=30𝑥

3 𝑥=303𝑥3

=303

𝑥=10

Page 37

𝟖

𝟏𝟐

𝟔

𝒙

812

=6𝑥

8 𝑥=728 𝑥8

=728

𝑥=9

Page 37

7 : 4

𝟕

𝟗𝟏𝟏

P=7+9+11P=27

𝟐𝟏

P=x

721

=27𝑥

7 𝑥=5677𝑥7

=5677

𝑥=81

Page 37

This means altitudes, medians, angle bisectors, etc…

Ratio of altitudes = ratio of sides = ratio of perimeters

614

=21𝑥

6 𝑥=2946 𝑥6

=2946

𝑥=49

Page 37

𝟔

𝟕𝟏𝟐

P=6+7+12P=25

𝒙

P=75

6𝑥

=2575

25 𝑥=45025𝑥25

=45025

𝑥=18

Homework

Page 37

#2,4,6,8,10,14,17

Separate Sheet

Page 37

5 :1

Ratio of medians = ratio of sides = ratio of perimeters

43=12𝑥

4 𝑥=364 𝑥4

=364

𝑥=9

Page 37

Ratio of altitudes = ratio of sides = ratio of perimeters

96=24𝑥

9 𝑥=1449𝑥9

=1449

𝑥=16

Page 37

𝟖

𝟏𝟎𝟏𝟐𝟔

𝒙68=𝑥12

8 𝑥=728 𝑥8

=728

𝑥=9

Page 37

𝒙

𝑥20

=8040

40𝑥=160040 𝑥40

=160040

𝑥=40

Page 37

𝟔

𝟖𝟏𝟎

P=6+8+10P=24

𝒙P=12

624

=𝑥12

24 𝑥=7224 𝑥24

=7224

𝑥=3

Page 37

𝟓

𝟖

𝑷=𝒙 𝑷=𝟐 𝒙−𝟏𝟎

Ratio of altitudes = ratio of sides = ratio of perimeters

5𝑥

=8

2𝑥−10

5 (2 𝑥−10 )=8 𝑥

10 𝑥−50=8𝑥−10 𝑥−10𝑥

−50=−2𝑥−50−2

=−2 𝑥−2

25=𝑥𝑷=𝟐𝟓 𝑷=𝟐 ∙𝟐𝟓−𝟏𝟎

𝑷=𝟒𝟎