Essential Question Learning Objective What does it mean to say that two figures are similar? Given...

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