ratio of similitude. the ratio of similitude of two similar polygons is the ratio of the lengths of...
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Ratio of Similitude
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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!
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Other segments that have the same ratio as the sides:
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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
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𝟑𝟎𝒙
31=30𝑥
3 𝑥=303𝑥3
=303
𝑥=10
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𝟖
𝟏𝟐
𝟔
𝒙
812
=6𝑥
8 𝑥=728 𝑥8
=728
𝑥=9
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7 : 4
𝟕
𝟗𝟏𝟏
P=7+9+11P=27
𝟐𝟏
P=x
721
=27𝑥
7 𝑥=5677𝑥7
=5677
𝑥=81
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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
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𝟔
𝟕𝟏𝟐
P=6+7+12P=25
𝒙
P=75
6𝑥
=2575
25 𝑥=45025𝑥25
=45025
𝑥=18
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Homework
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#2,4,6,8,10,14,17
Separate Sheet
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5 :1
Ratio of medians = ratio of sides = ratio of perimeters
43=12𝑥
4 𝑥=364 𝑥4
=364
𝑥=9
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Ratio of altitudes = ratio of sides = ratio of perimeters
96=24𝑥
9 𝑥=1449𝑥9
=1449
𝑥=16
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𝟖
𝟏𝟎𝟏𝟐𝟔
𝒙68=𝑥12
8 𝑥=728 𝑥8
=728
𝑥=9
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𝒙
𝑥20
=8040
40𝑥=160040 𝑥40
=160040
𝑥=40
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𝟔
𝟖𝟏𝟎
P=6+8+10P=24
𝒙P=12
624
=𝑥12
24 𝑥=7224 𝑥24
=7224
𝑥=3
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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