Bellwork Find the geometric mean of 32 & 5 Find the geometric mean of 75 & 18 What are the new coordinates for a dilation of an object with

vertices (2,3), (5,4) & (-2,5) if a scale factor of 5 is used? Bill kicks a ball in a straight line towards the top of a building.

Bob is standing nearby and the ball nearly misses his head. Bob is 6 feet tall and the building is 20 feet tall. If Bob is standing 15 feet away from Bill, how far away is Bob from the building?

Bellwork Solution Find the geometric mean of 32 & 5

32 5 x2 16 5 x4 10x

Bellwork Solution Find the geometric mean of 75 & 18

75 18 x25 3 9 2 x5 3 3 2 x15 6x

Bellwork Solution What are the new coordinates for a dilation of an object with

vertices (2,3), (5,4) & (-2,5) if a scale factor of 5 is used?

(2,3)

(5,4)

( 2,5)

(10,15)

(25,20)

( 10,25)

Bellwork Solution Bill kicks a ball in a straight line towards the top of the building.

Bob is standing nearby and the ball nearly misses his head. Bob is 6 feet tall and the building is 20 feet tall. If Bob is standing 15 feet away from Bill, how far away is Bob from the building?

6 15

20 156(15 ) 300

x

xBuilding

6

15

20

x

90 6 300 x6 210x

35x ft

TEST PREPARATIONDAY

Chapter 6

TEST ON WEDNESDAY

Example

Find the exact geometric mean for 6 & 22

.11.49

.2 66

.2 33

A

B

C

Example

Find the exact geometric mean for 56 & 22

.18 2

. 66

.6 18

A

B

C

ExampleAssuming a similar ratio exists, find the measure of FE

A

B C

DE

FG

H

2

3

6

5

x+1

12

2y+2

.6.33

.7

.8

A

B

C

ExampleAssuming a similar ratio exists, find the measure of EF

A

B

C

D

E

F

10

1416

x+1 x

2x-9

..5

.7

.14

A

B

C

ExampleGiven ▲ABC~▲DCA, solve for x

A

B

C

D

x

36

9 .9

.18

.324

A

B

C

ExampleThe object on the left is scaled by a factor of 3.75. What is the

length of the corresponding side to AB of the new figure?

15 11

16

19

.4

.71.25

.76

.90.25

A

B

C

D

A

B

C

D

ExampleWhat is the perimeter of object 2

15

.18.75

.36

.44

.48

A

B

C

D

1P=55

2 12

ExampleAre these two triangles similar?

12

8

918

12

13.5

. ,

. ,

. ,

.

AYes SSS

B Yes SAS

C Yes AA

D No

Example

. ,

. ,

. ,

.

AYes SSS

B Yes SAS

C Yes AA

D No

Are these two triangles similar?

15

9 13

19

Example

. ,

. ,

. ,

.

AYes SSS

B Yes SAS

C Yes AA

D No

Are these two triangles similar?

18

9

7

7

Example

. ,

. ,

. ,

.

AYes SSS

B Yes SAS

C Yes AA

D No

Are these two triangles similar?

A

B

C

D E45

22.5 20

22

ExampleWhat value of x makes the lines parallel?

18

x+3

8x-1

6

.2

.4

.13.33

A

B

C

ExampleWhat value of x makes the lines parallel?

27

5

15x

x

. 3

.3

.9

.135

A

B

C

D

ExampleWhat value of x makes the lines parallel?

..285

.1.33

.3.42

.4.17

A

B

C

D

1219

xx+2

ExampleWhat value of x makes the lines parallel?

.3

.4.24

.5.5

.6

A

B

C

D

x-54

2x+2

ExampleWhat is the scale factor between these two objects?

16

3.44

.3

.1.33

.4

A

B

C

D

12 12

Example

If a 50 meter building produces a shadow that is 30 meters in length, how long of a shadow will be produced by a 1.75m individual

.1.05

.2.5

.2.92

.3.2

A m

B m

C m

D m

ExampleWhat is the k factor of the dilation?

3.22

.3

.2

.3

A

B

C

D

1

2

Y

X

Y

X

ExampleWhat is the coordinate of the image of a dilation if the original

coordinate was (-3,5) and the k factor is 3?

.( 9,15)

.( 9,5)

.( 3,15)

.(9, 15)

A

B

C

D

ExampleYou want to create a quadrilateral RSTU that is similar to

quadrilateral ABCD. What are the coordinates of U?

Homework

Recommended Chapter Review 1-21