Chapter 8:

SIMILARITY

Similar Triangles in the

Real World

Nature

Art and Craft

Structures we design and build.

Similar Triangles turn up in

the strangest of places,

Amazing Similar Triangles

are found inside the crystals

of the beautifully colored

“Tourmaline” gemstone.

Similar Cars https://youtu.be/XtkU4VkWh8I scale factor by edkolu

In this lesson we look at the

nature of similar figures,

concentrating on Similar

Triangles.

SIMILAR TRIANGLES

Two figures are similar (symbol is ___) when

All corresponding angles are _______

All corresponding sides are _________

Therefore, similar figures have the same

________, but are not necessarily the same

__________.

The scale factor K or coefficient of

proportionality is equal to the ratio of the

measures of two corresponding sides.

K = ____ or ______

Proportionality

1

2=

2

4=

4

8=

8

16= ____ = _____ = _____

Are the following proportional?

1.) 4

6=

8

12

2.) 5

6=

29

30

3.) 10

90=

1

9

4.) 4

60=

2

30

If you obtain 18

25𝑜𝑛 𝑎 𝑡𝑒𝑠𝑡, 𝑤ℎ𝑎𝑡 𝑖𝑠 𝑦𝑜𝑢𝑟 %?

Find the value of 𝑥 if both fractions

are proportional.

1. 𝑥

6=

8

12

2. 4

2𝑥=

8

9

3. 3

500=

3𝑥

2𝑥−6

4. 𝑥

5=

40

10𝑥

Homework Similarity

Booklet Page 1

Determine the value of x, if similarity

exists. (Space 5 lines each)

4)

5) Determine the value of x.

Solution

5) Determine the value of x. Skip? Repeat of #4

If time permits, real life

situation.

If time permits, real life

situation.

If time permits, real life

situation.

Answer in feet.

Homework Similarity

Booklet Page 2-8

If 𝐵𝐷̅̅ ̅̅ //𝐴𝐸̅̅ ̅̅ , then 𝐵𝐶̅̅ ̅̅

𝐴𝐵̅̅ ̅̅=

𝐶𝐷̅̅ ̅̅

𝐷𝐸̅̅ ̅̅

Ex: Find the Value of x.

Example: Explain why Thales Theorem

does NOT apply and then solve for 𝑥.

Homework Similarity

Booklet Page 9- 25

Congruency Proof

Prove ∆𝐴𝐵𝐷 ≅ ∆BCD

Prove ∆𝐴𝐵𝐷 ≅ ∆BCD

Similarity Proof

Prove ∆𝐺𝐿𝐻~∆GFE

Prove ∆𝐴𝐵𝐷~∆DEF

Homework Similarity

Booklet Page 26 - END