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Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

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Page 1: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles
Page 2: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportion

& Ratios

$100

$200

$300

$500

$400

Similar

Polygons

$400

$300

$200

$100

$500

Similar

Triangles

$100

$200

$300

$400

$500

Proportions in Triangles

$100

$200

$300

$400

$500

Page 3: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions for $100

Two ratios that are equal

Page 4: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions for $200

4

7 35m

Page 5: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions for $300

Find the ratio of the length to the width of the rectangle and simplify.

60 feet

78 feet

Page 6: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions for $400

The similarity ratio of two rectangles is 4:5. What is the ratio of the perimeters

and the areas?

Page 7: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

The area of a regular octagon is 35 cm2. What is the area of a regular octagon with side six

times as large?

Page 8: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Polygons for $100

If two polygons are similar then

1) Corresponding __________ are congruent

and

2) Corresponding sides are __________.

Page 9: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Polygons for $200

Determine if the two figures are similar and

explain:

10 cm

20 cm

5 cm

10 cm

Page 10: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Polygons for $300

The measures of the corresponding sides of the polygons are proportional. If AD = 6, DC = 3, and WZ = 33, find YZ. (not drawn to scale)

D

A

B

C W

X

Z

Y

Page 11: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Polygons for $400

The two polygons are similar. Find the value of x.

15

18

30

x

Page 12: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Polygons for $500

The polygons below are similar, but not necessarily drawn to

scale. Find the values of x and y.

20

45

x-1

y+1

12

9

21

27

Page 13: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Triangles for $100

What are the three different ways to prove triangles similar?

AND

Are equilateral triangles always similar? What would be the easiest way to prove your

answer?

Page 14: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Triangles for $200

Are the two triangles similar? If so, tell which theorem you used

and explain why.

S

M

T

R

N

Page 15: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Triangles for $300

Are the triangles similar? If so, tell which theorem you used and explain

why.

23

3 1/3

8

35

Page 16: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Triangles for $400

Explain why the triangles are similar. Then find the

value of x.

5

3

25º

x

4.525º

Page 17: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Similar Triangles for $500Campsites F and G are on opposite sides of a lake. A survey crew made the measurements shown on the diagram. What is the distance between the two campsites? The diagram is

not scale. F

G

47m

82m

92m 73.8m

82.8m

Page 18: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions in Triangles for $100

Use the Side-Splitter Theorem to find x

given that PQ || BC.A

P Q

B C

8 12

x18

Page 19: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions in Triangles for $200

Given AE || BD solve for x

A

ED C

B

x

5

11

7

Page 20: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions in Triangles for $300

Find x to the nearest tenth. Given that angle BAC is congruent to angle CAD

A

B

C

D

15.7

x

9.6

20.2

Page 21: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions in Triangles for $400

Solve for x and y

16.5

y

1526

x30

Page 22: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

Proportions in Triangles for $500

In Lexington Main Street, Vine Street, and High Street are parallel streets that intersect South and North Upper. How long is the walk from

Main Street to Vine Street along South Upper?

High St

Main St

Vine St

North UpperSouth Upper

330ft

500ft

425ft

Page 23: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles
Page 24: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles
Page 25: Proportion & Ratios $100 $200 $300 $500 $400 Similar Polygons $400 $300 $200 $100 $500 Similar Triangles $100 $200 $300 $400 $500 Proportions in Triangles

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