Essential Question Learning Objective What does it mean to say that two figures are similar? Given...
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![Page 1: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/1.jpg)
Essential Question
Learning Objective
What does it mean to say that two figures are similar?
Given two figures, I will determine whether or not they are similar and state my reasoning.
![Page 2: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/2.jpg)
Transformations
Reflections
![Page 3: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/3.jpg)
TransformationsTranslations
![Page 4: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/4.jpg)
TransformationsRotations
90o
![Page 5: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/5.jpg)
TransformationsDilations
![Page 6: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/6.jpg)
Transformations
Reflections
Translations
Rotations
Dilations
![Page 7: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/7.jpg)
![Page 8: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/8.jpg)
you should know:
what you've learned: What is perimeter and areahow to calculate perimeter and area of rectangles, squares, and trianglesundefined terms: point, line, planedefined terms: segment, ray, angle, parallel, perpendicularangle pair relationships: complementary, supplementary, linear pair, vertical anglesTransformations: (reflections, translations, rotations) & (dilations)CongruenceTriangle congruence shortcuts: SSS, SAS, ASATriangle Facts: Triangle Sum, 3rd Angles ≅Constructions: ≅ segments, ≅ triangles, perpendicular bisectors, ≅ angles, angle bisectors, parallel segments, equilateral triangles, regular hexagon, square
Similarity
6.3 Similarity
![Page 9: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/9.jpg)
Scale factor can be written as a decimal or as a fraction:
64
57.5
2.8
4.2
preimageimage
Scale Factor
or .6667
imagepreimage
or 2.5
33
4
7.5
7.5
10
![Page 10: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/10.jpg)
You can calculate scale factor by dividing the image lengths from the pre-image lengths:
Scale Factor
imagepreimage
or 2.5
33
4
10
7.5
7.5
7.5 / 3 = 2.5
7.5 / 3 = 2.5
10 / 4 = 2.5
![Page 11: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/11.jpg)
Key Terms:
Similarity -
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Key Terms:
Similarity -
Ratio - a comparison of two numbers using division.
a
ba : b a to b
Corresponding sides all have the same scale factor and corresponding angles are congruent.
Proportionality - an equation that states that two or more ratios are equal.
![Page 13: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/13.jpg)
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"WE DO" TIME
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Problem
a) b)
c) d)
What is the symbol of similarity?
≅
T
˜Δ
![Page 19: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/19.jpg)
Problem
Are the triangles similar? Why?
105o
45o30
o
105o 45
o30o
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Problem
Are the triangles similar? Why?
80o
80o
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Problem
Are the triangles similar? Why?
52o
24o
52o
24o
![Page 22: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/22.jpg)
Problem
Are the triangles similar? Why?
![Page 23: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/23.jpg)
Problem
Are the triangles similar? Why?
97o
56o
27o
97o
![Page 24: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/24.jpg)
Problem
Are the triangles similar? Why?
54o
70o
56o
52o
73o54
o
![Page 25: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/25.jpg)
Problem
Are the triangles similar? Why?
43
6
5.5
11
8
![Page 26: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/26.jpg)
Problem
Are the triangles similar? Why?
3
515
9
![Page 27: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/27.jpg)
Problem
Are the triangles similar? Why?
13
6
6.5
8.4
18.2
3.2
![Page 28: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/28.jpg)
Problem
Are the triangles similar? Why?
10
7.7
6
4.62
3.6
![Page 29: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/29.jpg)
Problem
Are the triangles similar? Why?
![Page 30: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/30.jpg)
Essential Question
Learning Objective
What does it mean to say that two figures are similar?
Given two figures, I will determine whether or not they are similar and state my reasoning.
![Page 31: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/31.jpg)
Closure
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HW
none
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A
B
C
A'
B'
C'
10
11
7.7
6.6
4.62
![Page 34: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/34.jpg)
64
57.5
2.8
4.2
A
B
C
D
E
F
![Page 35: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/35.jpg)
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A
C
B
2
3
3.5
4
7
A'
B'
C'
![Page 37: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/37.jpg)
sim by angles
three angles given
two angles
not similiar
![Page 38: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/38.jpg)
sim by sides
three sides
two sides
not sim
![Page 39: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/39.jpg)
A
B
C
A'
B'
C'
4.5
6
7.6
11.25 15
19
![Page 40: Essential Question Learning Objective What does it mean to say that two figures are similar? Given two figures, I will determine whether or not they are.](https://reader036.fdocuments.in/reader036/viewer/2022062519/5697bfeb1a28abf838cb7a9e/html5/thumbnails/40.jpg)
5
45.5 2
2.5
2.75
6
2
12.2
46.6
59o
59o
61o
61o