**Lesson 6.6**

**Chapter 6**

**By: Caroline T. and Kaan A.**

**Lesson 6.1**

~Use similar polygons~

**Lesson 6.2**

~relate transformations and similarity~

Prove Triangles similar by AA

**Similarity**

**~**

**Lesson 6.3**

**lesson 6.4**

Prove triangles similar by SSS and SAS

What are similar polygons?

Similar polygons are polygons that have congruent corresponding angles, and the corresponding sides are proportional.

Preform similarity transformations

Example 1

Use Similarity Statements

ABC~EGF

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6

12

20

3

10

can you:

a) List all pairs of congruent angles.

b) Check that the ratios of corresponding side lengths are congruent.

c) Write the ratios of the corresponding side lengths in a

statement of proportionality

.

Example 1

~ means similar

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30

A

B

C

D

E

10

x

Example 2

Find the scale factor

y

3

6

12

20

6

10

I wonder what the scale factor is. I think that it is 1:2.

Can you:

1) figure out the scale factor

2) Figure out the values of x and y

To find the scale factor, you need to take a pair of corresponding sides and put them like this:

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3

Then you simplify, the scale factor is 2. If you multiply the little triangle by 2, you get the big triangle.

Example 2

Example 3

Use Similar Polygons

A

B

C

F

D

E

10

20

10

18

4

x

AHHH!

We don't know the length of one of the sides! What are we going to do?

Mr. Penguin, you can set up a proportion to solve it.

10

20

=

4

Explain why Mr. Penguin Is wrong

x

10x=80

x=8

ABC~DEF

100

50

For your notebook:

Similar polygons have congruent corresponding angles and proportional corresponding sides

To find the scale factor, you can set up a fraction and solve it.

To find the missing variable side length, you can set up a proportion and solve it.

The difference between similarity ratio and

Oh yeah! Also, the perimeter ratio will be the same as your similarity ratio, however, the area ratio will be both of the numbers squared!

For your notebook

Have you been paying attention?

**Detour!**

This is a huge quiz worth 0 points!

1) Find x.

2) Find y.

x

5

y

27

9

Assume triangles ABC and EGF are similar!

45

65

Answers:

x=70

y=15

If dilation can be used to move one figure into another, the two figures are similar.

If dilation followed by any combination of rigid motions can be used to move one figure into another, the two figures are similar.

BD is || to CE

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10

scale factor, is the scale factor is what you

multiply one to get to the other. Similarity

ratio the ratio from one to the other.

**Thanks for watching!**

Explain why Mr. Penguin is wrong

Example 1

Example 1

Use the AA similarity Shortcut

8

12

16

12

6

9

8

10

16

1) explain why Mr. Penguin is wrong?

All of these triangles are similar

2) find the similarity ratio from the two similar triangles from little to big?

50

20

40

A

B

C

D

E

1) use SSS to prove similar

2) use SAS to prove similar

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Assume DE is || to AB

For your notebook

SSS similarity = If the corresponding side lengths of two triangles are proportional, then the two triangles are similar

SAS similarity = If an angle of one triangle is congruent to an angle of an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar

PQRS~TUVW

by a dilation

P (4, 8)

Q (1,7)

R (0,-1)

S (-11, 6)

Example 1

T (3, 6)

U (

V

W (

uh-oh! I am blocking the coordinates of U, v, and t. What are their values?

Example 2

Draw a dilation of ABC with similarity ratio 2/5

A (-2, 1)

B (-4, 1)

C (-2, 4)

For your notebook

You can describe a dilation with respect to the origin with the notation (x, y)→(kx, ky) where k is the scale factor

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100

100

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What do the angles of a triangle add up to?

If we know two angles, we can find the third because the angles of a triangle will always add up to 180º.

For your Notebook

1) If two pairs of corresponding angles are congruent, then the two triangles are similar.

2) This is solved by if there are two pairs of congruent angles, then the third angle must be congruent due to the third angle theorem.

CAN YOU:

CAN YOU:

Example 2

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