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Warm Up

Problem of the Day

Presentation Six Lessons

Warm Up Find the cross products, then tell

whether the ratios are equal.

16 6

40 15

,

1.

240 240 equal

3 8

18 46

,

2.

8 9

24 27

,

3.

216 216 equal

28 12

42 18

,

4.

504 504 equal

Problem of the Day Every 8th telephone pole along

a road has a red band painted on it. Every 14th

pole has an emergency call phone on it. What is

the number of the first pole with both a red band

and a call phone?

56

Lesson 1 EQ How can I determine if two figures

are similar?

Insert Lesson Title Here

Vocabulary Words

similar corresponding sides corresponding angles

Similarity in the Real World

Octahedral fluorite is a crystal found in nature.

It grows in the shape of an octahedron, which is

a solid figure with eight triangular faces. The

triangles in different-sized fluorite crystals

are similar figures. Similar figures have the

same shape but not necessarily the same size.

Vocabulary

SIMILAR FIGURES

Two figures are similar if The measures of their corresponding angles are equal. The ratios of the lengths of the corresponding sides are proportional.

Vocabulary

Matching sides of two or more polygons are called

corresponding sides, and matching angles are

called corresponding angles.

Symbols

?ABC

AB

and

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Example 1 Determining Whether Two Triangles Are

Similar

Identify the corresponding sides in the pair of

triangles. Then use ratios to determine whether

the triangles are similar.

E

16 in

10 in

A

C

28 in

D

4 in

7 in

40 in

F

B

AB DE

BC EF

AC DF

Step 1 Write ratios using the corresponding

sides.

4 16

7 28

10 40

Step 2 Substitute the length of the sides.

1 4

1 4

1 4

Step 3 Simplify each ratio.

Since the ratios of the corresponding sides are

equivalent, the triangles are similar.

Check It Out Example 2

Identify the corresponding sides in the pair of

triangles. Then use ratios to determine whether

the triangles are similar.

E

9 in

9 in

A

C

21 in

D

3 in

7 in

27 in

F

B

AB DE

BC EF

AC DF

Write ratios using the corresponding sides.

3 9

7 21

9 27

Substitute the length of the sides.

1 3

1 3

1 3

Simplify each ratio.

Since the ratios of the corresponding sides are

equivalent, the triangles are similar.

Lesson 2 EQ How can I determine if figures are

similar based on their angle measure?

How can I determine if these shapes are similar?

Tell whether the figures are similar.

Yes.The corresponding angles of the figures

have equal measure.

D

60

F

E

A

60

remember the sum of the interior angles of a

triangle 180

C

B

Insert Lesson Title Here

Try One

Tell whether the figures are similar. (Notice the

shapes are turned) 1.

similar

Insert Lesson Title Here

Try another

Tell whether the figures are similar. 2.

not similar

Lesson 3 EQ How can I determine the scale

factor of similar figures?

Vocabulary

Scale Factor The ratio of the lengths of

corresponding sides in similar figures

How can I determine the scale factor of similar

figures?

EXAMPLE 1 The figures below are similar

3

4

How can I determine the scale factor of similar

figures?

EXAMPLE 2 A B

2.5

A

5

B

2

1

Lesson 4 EQ What is the relationship between

the scale factor, side lengths, perimeter, and

area?

The relationship between scale factor, side

lengths, perimeter, and area...

5.5 ft

Figure A B Ratio/Scale Factor

Corresponding Sides

Side Lengths (feet)

Perimeter

Area

11 ft

3 ft

6 ft

5 ft

10 ft

The scale factor tells you the ratio of

corresponding side lengths and the ratio of the

perimeters The scale factor SQUARED tells you

the ratio of the areas

Lesson 5 EQ How can I determine missing side

lengths of similar figures?

Example 1 Missing Side Lengths

Find the unknown length in similar figures.

AC QS

AB QR

Step 1 Write a proportion using corresponding

sides.

12 48

14 w

Step 2 Substitute lengths of the sides.

12 w 48 14

Step 3 Cross multiply and divide.

12w 672

12w 12

672 12

Divide each side by 12 to isolate the variable.

w 56

QR is 56 centimeters.

Insert Lesson Title Here

Check It Out Example 2

Find the unknown length in similar figures.

x

Q

R

10 cm

A

B

24 cm

12 cm

D

C

T

S

AC QS

AB QR

Write a proportion using corresponding sides.

12 24

10 x

Substitute lengths of the sides.

12 x 24 10

Find the cross product.

12x 240

Multiply.

12x 12

240 12

Divide each side by 12 to isolate the variable.

x 20

QR is 20 centimeters.

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Example 3 Measurement Application

The inside triangle is similar in shape to the

outside triangle. Find the length of the base of

the inside triangle.

Let x the base of the inside triangle.

8 2

12 x

Write a proportion using corresponding

side lengths.

8 x 2 12

Find the cross products.

8x 24

Multiply.

8x 8

24 8

Divide each side by 8 to isolate the variable.

x 3

The base of the inside triangle is 3 inches.

Insert Lesson Title Here

Example 4

The rectangle on the left is similar in shape to

the rectangle on the right. Find the width of the

right rectangle.

12 cm

6 cm

3 cm

?

Let w the width of the right rectangle.

6 12

3 w

Write a proportion using corresponding side

lengths.

6 w 12 3

Find the cross products.

Multiply.

6w 36

36 6

6w 6

Divide each side by 6 to isolate the variable.

w 6

The right rectangle is 6 cm wide.

Insert Lesson Title Here

Ticket-out-the-door

Find the unknown length in each pair of similar

figures.

1.

2.

Insert Lesson Title Here

Ticket-out-the-door

Find the unknown length in each pair of similar

figures.

3. The width of the smaller rectangular cake is

5.75 in. The width of a larger rectangular cake

is 9.25 in. Estimate the length of the larger

rectangular cake.

Lesson 6 EQ How can I use shadow math to find

missing side lengths?

Example 1 Missing Side Lengths

Step 1 Label Corresponding Parts.

Step 2 Write a Proportion.

Step 3 Cross multiply and divide.

x

1.5m

5m

1m

Additional Example 2 Estimating with Indirect

Measurement

City officials want to know the height of a

traffic light. Estimate the height of the traffic

light.

48.75 h

27.25 15

Step 1 Label Corresponding Parts.

27 15

49 h

h ft

9 5

49 h

Step 2 Write a Proportion

27.25 ft

9h 245

Step 3 Cross multiply.

48.75 ft

h 27

Multiply each side by 9 to isolate the variable.

The traffic light is about 30 feet tall.

Check It Out Example 3

The inside triangle is similar in shape to the

outside triangle. These are called NESTED

triangles. Find the height of the outside

triangle.

h 30.25

5 14.75

Write a proportion.

Use compatible numbers to estimate.

5 15

h 30

h ft

5 ft

13

h 30

Simplify.

Cross multiply.

1 30 3 h

14.75 ft

Multiply each side by 5 to isolate the variable.

30 3h

30.25 ft

10 h

The outside triangle is about 10 feet tall.

Classwork

- Problem 5.1(pg.78-79)
- Problem 5.2 (pg. 80-81)
- Problem 5.3 (pg. 82-83)