55

66

44

881010

1212

CC

AA BB

XX

ZZ

YY

ExerciseExercise∆XYZ ~ ∆LMN. Dimensions are in inches. Find LM.∆XYZ ~ ∆LMN. Dimensions are in inches. Find LM. 6 in.6 in.

10L P

M

N

20X W

Y

Z

16129.6

∆XYZ ~ ∆LMN. Dimensions are in inches. Find MP.∆XYZ ~ ∆LMN. Dimensions are in inches. Find MP. 4.8 in.4.8 in.

10L P

M

N

20X W

Y

Z

16129.6

ExerciseExercise

What is the ratio of the perimeter of ∆XYZ to the perimeter of ∆LMN?

What is the ratio of the perimeter of ∆XYZ to the perimeter of ∆LMN? 2 : 12 : 1

10L

M

N

20X

Y

Z

1612

ExerciseExercise

9.6

Find the area of of ∆LMN.Find the area of of ∆LMN.

24 in.224 in.2

9.6

ExerciseExercise

10L

M

N

20X

Y

Z

1612

What is the ratio of the area of ∆XYZ to the area of ∆LMN?What is the ratio of the area of ∆XYZ to the area of ∆LMN?

4 : 14 : 1

ExerciseExercise

10L

M

N

20X

Y

Z

1612 9.6

The ratio of the perimeters is equal to the ratio of the corresponding sides.

The ratio of the perimeters is equal to the ratio of the corresponding sides.

Ratio of the Perimeters of Similar PolygonsRatio of the Perimeters of Similar Polygons

The corresponding sides of two similar triangles are 16 in. and 12 in. The perimeter of the first triangle is 55 in. Find the perimeter of the second triangle, p2.

The corresponding sides of two similar triangles are 16 in. and 12 in. The perimeter of the first triangle is 55 in. Find the perimeter of the second triangle, p2.

16121612 == 4

343

Example 1Example 1

p2 = 41.25 in.p2 = 41.25 in.

16121612 == 4

3434343 == 55

p2

55p2

4p2 = 3(55)4p2 = 3(55)

4p2 = 1654p2 = 16544 44

The perimeters of two similar hexagons are 20 ft. and 180 ft. The smaller hexagon has one side of 2 ft. Find the corresponding side of the larger hexagon.

The perimeters of two similar hexagons are 20 ft. and 180 ft. The smaller hexagon has one side of 2 ft. Find the corresponding side of the larger hexagon.

2s2s == 20

18020

180

Example 2Example 2

2s2s == 1

919

2s2s == 20

18020

180

s = 18 ft.s = 18 ft.

s = 2(9)s = 2(9)

For the figure, write the missing factor: EF = __BC.

For the figure, write the missing factor: EF = __BC.

33

A

4 CB 12E F

D

ExampleExample

4

6a6a

66

4a4a

The ratio of the areas of similar polygons is equal to the ratio of the squares of the corresponding sides.

The ratio of the areas of similar polygons is equal to the ratio of the squares of the corresponding sides.

Ratio of the Areas of Similar PolygonsRatio of the Areas of Similar Polygons

( )( )

The first of two regular pentagons has a side of 4 cm, and the second has a side of 3 cm. What is the ratio of their areas?

The first of two regular pentagons has a side of 4 cm, and the second has a side of 3 cm. What is the ratio of their areas?

==4343

4343

4343

169

169==××

22

Example 3Example 3

The first of two similar polygons has a side of 3 cm and an area of 10 cm2. The corresponding side of the second is 5 cm. What is the area of the second polygon?

The first of two similar polygons has a side of 3 cm and an area of 10 cm2. The corresponding side of the second is 5 cm. What is the area of the second polygon?

( )( )10A2

10A2

== 3535

22

Example 4Example 4

A2 ≈ 27.8 cm2A2 ≈ 27.8 cm2

10A2

10A2

== 9259

25

9A2 = 10(25)9A2 = 10(25)

9A2 = 2509A2 = 25099 99

The areas of two similar pentagons are 400 mm2 and 100 mm2. One side of the smaller pentagon is 9 mm. Find the length of the similar side of the larger pentagon.

The areas of two similar pentagons are 400 mm2 and 100 mm2. One side of the smaller pentagon is 9 mm. Find the length of the similar side of the larger pentagon.

( )( )s9s9

400100400100 ==

22

Example 5Example 5

s = 18 mms = 18 mm

4141 == s2

81s2

81

s2 = 4(81)s2 = 4(81)

s2 = 324s2 = 324

s = 324 s = 324

∆ABC ~ ∆DEF. For the figure, write the missing factor: area of ∆DEF = __ area of ∆ABC.

∆ABC ~ ∆DEF. For the figure, write the missing factor: area of ∆DEF = __ area of ∆ABC.

99

A

4 CB12E F

D

ExampleExample

∆ABC ~ ∆DEF. If the area of ∆ABC is 8 units2, what is the area of ∆DEF?

∆ABC ~ ∆DEF. If the area of ∆ABC is 8 units2, what is the area of ∆DEF?

ExampleExample

72 units2 72 units2

A

4 CB12E F

D

∆ABC ~ ∆DEF. If the perimeter of ∆ABC is 14 units, what is the perimeter of ∆DEF?

∆ABC ~ ∆DEF. If the perimeter of ∆ABC is 14 units, what is the perimeter of ∆DEF?

ExampleExample

A

4 CB12E F

D

42 units42 units

There are 640 acres in a square mile. How many acres are in a parcel of land that is mi. × mi.?

There are 640 acres in a square mile. How many acres are in a parcel of land that is mi. × mi.?1212

1212

ExampleExample

160 acres160 acres

How many square inches are in a rectangle that is 2 ft. × 3 ft.?

How many square inches are in a rectangle that is 2 ft. × 3 ft.?

ExampleExample

864 in.2 864 in.2

How many square feet are in 288 in.2?How many square feet are in 288 in.2?

ExampleExample

2 ft.2 2 ft.2

How many square feet are in a square yard? How many square inches are in a square yard?

How many square feet are in a square yard? How many square inches are in a square yard?

9 ft.2; 1,296 in.29 ft.2; 1,296 in.2

ExampleExample