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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.
Transformations
Reflections
TransformationsTranslations
TransformationsRotations
90o
TransformationsDilations
Transformations
Reflections
Translations
Rotations
Dilations
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
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
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
Key Terms:
Similarity -
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.
"WE DO" TIME
Problem
a) b)
c) d)
What is the symbol of similarity?
≅
T
˜Δ
Problem
Are the triangles similar? Why?
105o
45o30
o
105o 45
o30o
Problem
Are the triangles similar? Why?
80o
80o
Problem
Are the triangles similar? Why?
52o
24o
52o
24o
Problem
Are the triangles similar? Why?
Problem
Are the triangles similar? Why?
97o
56o
27o
97o
Problem
Are the triangles similar? Why?
54o
70o
56o
52o
73o54
o
Problem
Are the triangles similar? Why?
43
6
5.5
11
8
Problem
Are the triangles similar? Why?
3
515
9
Problem
Are the triangles similar? Why?
13
6
6.5
8.4
18.2
3.2
Problem
Are the triangles similar? Why?
10
7.7
6
4.62
3.6
Problem
Are the triangles similar? Why?
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.
Closure
HW
none
A
B
C
A'
B'
C'
10
11
7.7
6.6
4.62
64
57.5
2.8
4.2
A
B
C
D
E
F
A
C
B
2
3
3.5
4
7
A'
B'
C'
sim by angles
three angles given
two angles
not similiar
sim by sides
three sides
two sides
not sim
A
B
C
A'
B'
C'
4.5
6
7.6
11.25 15
19
5
45.5 2
2.5
2.75
6
2
12.2
46.6
59o
59o
61o
61o