Similar Figures (Not exactly the same, but pretty close!)
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![Page 1: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/1.jpg)
Similar Figures
(Not exactly the same, but pretty close!)
![Page 2: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/2.jpg)
Let’s do a little review work
before discussing similar figures.
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Congruent Figures
• In order to be congruent, two figures must be the same size and same shape.
![Page 4: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/4.jpg)
Similar Figures
• Similar figures must be the same shape, but their sizes may be different.
![Page 5: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/5.jpg)
Similar Figures This is the symbol that
means “similar.”
These figures are the same shape but different sizes.
![Page 6: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/6.jpg)
SIZES• Although the size of the two
shapes can be different, the sizes of the two shapes must differ by a factor.
3 3
2
1
6 6
2
4
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SIZES• In this case, the factor is x 2.
3 3
2
1
6 6
2
4
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SIZES• Or you can think of the
factor as 2.
3 3
2
1
6 6
2
4
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Enlargements• When you have a photograph
enlarged, you make a similar photograph.
X 3
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Reductions• A photograph can also be
shrunk to produce a slide.
4
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Determine the length of the unknown side.
12
9
15
4
3
?
![Page 12: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/12.jpg)
These triangles differ by a factor of 3.
12
9
15
4
3
?
15 3= 5
![Page 13: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/13.jpg)
Determine the length of the unknown side.
4
224
?
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These dodecagons differ by a factor of 6.
4
224
?
2 x 6 = 12
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Sometimes the factor between 2 figures is not obvious and some
calculations are necessary.
18
12 15
12
108
? =
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To find this missing factor, divide 18 by 12.
18
12 15
12
108
? =
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18 divided by 12 = 1.5
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The value of the missing factor is 1.5.
18
12 15
12
108
1.5 =
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When changing the size of a figure, will the angles of the
figure also change?
? ?
?
70 70
40
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Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180
degrees.If the size of the
angles were increased,the sum
would exceed180
degrees.70 70
40
70 70
40
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70 70
40
We can verify this fact by placing the smaller triangle inside the
larger triangle.
70 70
40
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70 70
70 70
40
The 40 degree angles are congruent.
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70 707070 70
40
40
The 70 degree angles are congruent.
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70 707070 70
40
4
The other 70 degree angles are congruent.
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Find the length of the missing side.
30
40
50
6
8
?
![Page 26: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/26.jpg)
This looks messy. Let’s translate the two triangles.
30
40
50
6
8
?
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Now “things” are easier to see.
30
40
50
8
?
6
![Page 28: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/28.jpg)
The common factor between these triangles is 5.
30
40
50
8
?
6
![Page 29: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/29.jpg)
So the length of the missing side
is…?
![Page 30: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/30.jpg)
That’s right! It’s ten!
30
40
50
8
10
6
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Similarity is used to answer real life questions.
• Suppose that you wanted to find the height of this tree.
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Unfortunately all that you have is a tape
measure, and you are too short to reach the
top of the tree.
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You can measure the length of the tree’s shadow.
10 feet
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Then, measure the length of your shadow.
10 feet 2 feet
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If you know how tall you are, then you can determine how tall
the tree is.
10 feet 2 feet6 ft
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The tree must be 30 ft tall. Boy, that’s a tall tree!
10 feet 2 feet6 ft
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Similar figures “work” just like equivalent fractions.
530
66 11
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These numerators and denominators differ by a factor of
6.
530
66 11
6
6
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Two equivalent fractions are called a proportion.
530
66 11
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Similar Figures
• So, similar figures are two figures that are the same shape and whose sides are proportional.
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Practice Time!
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1) Determine the missing side of the triangle.
3
4
5
12
9?
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1) Determine the missing side of the triangle.
3
4
5
12
915
![Page 44: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/44.jpg)
2) Determine the missing side of the triangle.
6
4
6 36 36
?
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2) Determine the missing side of the triangle.
6
4
6 36 36
24
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3) Determine the missing sides of the triangle.
39
24
33?
8
?
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3) Determine the missing sides of the triangle.
39
24
3313
8
11
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4) Determine the height of the lighthouse.
2.5
8
10
?
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4) Determine the height of the lighthouse.
2.5
8
10
32
![Page 50: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/50.jpg)
5) Determine the height of the car.
5
3
12
?
![Page 51: Similar Figures (Not exactly the same, but pretty close!)](https://reader035.fdocuments.us/reader035/viewer/2022062619/55155b52550346486b8b46c3/html5/thumbnails/51.jpg)
5) Determine the height of the car.
5
3
12
7.2
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THE END!