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![Page 1: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/1.jpg)
Similar Figures
(Not exactly the same, but pretty close!)
![Page 2: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/2.jpg)
Let’s do a little review work
before discussing similar figures.
![Page 3: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/3.jpg)
Congruent Figures
• In order to be congruent, two figures must be the same size and same shape.
![Page 4: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/4.jpg)
Similar Figures
• Similar figures must be the same shape, but their sizes may be different.
![Page 5: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/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](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/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
![Page 7: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/7.jpg)
SIZES• In this case, the factor is x 2.
3 3
2
1
6 6
2
4
![Page 8: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/8.jpg)
SIZES• Or you can think of the
factor as 2.
3 3
2
1
6 6
2
4
![Page 9: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/9.jpg)
Enlargements• When you have a photograph
enlarged, you make a similar photograph.
X 3
![Page 10: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/10.jpg)
Reductions• A photograph can also be
shrunk to produce a slide.
4
![Page 11: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/11.jpg)
Determine the length of the unknown side.
12
9
15
4
3
?
![Page 12: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/12.jpg)
These triangles differ by a factor of 3.
12
9
15
4
3
?
15 3= 5
![Page 13: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/13.jpg)
Determine the length of the unknown side.
4
224
?
![Page 14: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/14.jpg)
These dodecagons differ by a factor of 6.
4
224
?
2 x 6 = 12
![Page 15: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/15.jpg)
When changing the size of a figure, will the angles of the
figure also change?
? ?
?
70 70
40
![Page 16: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/16.jpg)
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
![Page 17: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/17.jpg)
70 70
40
We can verify this fact by placing the smaller triangle inside the
larger triangle.
70 70
40
![Page 18: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/18.jpg)
70 70
70 70
40
The 40 degree angles are congruent.
![Page 19: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/19.jpg)
70 707070 70
40
40
The 70 degree angles are congruent.
![Page 20: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/20.jpg)
70 707070 70
40
4
The other 70 degree angles are congruent.
![Page 21: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/21.jpg)
Find the length of the missing side.
30
40
50
6
8
?
![Page 22: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/22.jpg)
This looks messy. Let’s translate the two triangles.
30
40
50
6
8
?
![Page 23: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/23.jpg)
Now “things” are easier to see.
30
40
50
8
?
6
![Page 24: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/24.jpg)
The common factor between these triangles is 5.
30
40
50
8
?
6
![Page 25: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/25.jpg)
So the length of the missing side
is…?
![Page 26: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/26.jpg)
That’s right! It’s ten!
30
40
50
8
10
6
![Page 27: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/27.jpg)
Similarity is used to answer real life questions.
• Suppose that you wanted to find the height of this tree.
![Page 28: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/28.jpg)
Unfortunately all that you have is a tape
measure, and you are too short to reach the
top of the tree.
![Page 29: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/29.jpg)
You can measure the length of the tree’s shadow.
10 feet
![Page 30: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/30.jpg)
Then, measure the length of your shadow.
10 feet 2 feet
![Page 31: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/31.jpg)
If you know how tall you are, then you can determine how tall
the tree is.
10 feet 2 feet6 ft
![Page 32: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/32.jpg)
The tree must be 30 ft tall. Boy, that’s a tall tree!
10 feet 2 feet6 ft
![Page 33: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/33.jpg)
Similar Figures
• So, similar figures are two figures that are the same shape and whose sides are proportional.
![Page 34: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/34.jpg)
Practice Time!
![Page 35: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/35.jpg)
1) Determine the missing side of the triangle.
3
4
5
12
9?
![Page 36: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/36.jpg)
1) Determine the missing side of the triangle.
3
4
5
12
915
![Page 37: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/37.jpg)
2) Determine the missing side of the triangle.
6
4
6 36 36
?
![Page 38: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/38.jpg)
2) Determine the missing side of the triangle.
6
4
6 36 36
24
![Page 39: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/39.jpg)
3) Determine the missing sides of the triangle.
39
24
33?
8
?
![Page 40: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/40.jpg)
3) Determine the missing sides of the triangle.
39
24
3313
8
11
![Page 41: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/41.jpg)
4.) Determine the missing side
![Page 42: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/42.jpg)
5.) Determine the missing side
![Page 43: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/43.jpg)
6) Determine the height of the lighthouse.
2.5
8
10
?
![Page 44: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/44.jpg)
6) Determine the height of the lighthouse.
2.5
8
10
32
![Page 45: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/45.jpg)
7) Determine the height of the car.
5
3
12
?
![Page 46: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/46.jpg)
7) Determine the height of the car.
5
3
12
7.2
![Page 47: Similar Figures](https://reader035.fdocuments.us/reader035/viewer/2022062422/56812cf3550346895d91c0a4/html5/thumbnails/47.jpg)
THE END!