chapter 6 resource masters...stages 1 and 2 of a fractal known as the cantor set are shown. to get...

$: Chapter 6 Resource Masters...Stages 1 and 2 of a fractal known as the Cantor set are shown. To get Stage 2, the segment in Stage 1 is trisected, and the interior of the middle segment$
© Glencoe/McGraw-Hill 298 Glencoe Geometry

1. NUTRITION One ounce of cheddar cheese contains 9 grams of fat. Six of the grams of fatare saturated fats. Find the ratio of saturated fats to total fat in an ounce of cheese.

2. FARMING The ratio of goats to sheep at a university research farm is 4:7. The numberof sheep at the farm is 28. What is the number of goats?

3. ART Edward Hopper’s oil on canvas painting Nighthawks has a length of 60 inches anda width of 30 inches. A print of the original has a length of 2.5 inches. What is the widthof the print?

Solve each proportion.

4. �58� � �1

x2� 5. �1.

x12� � �

15� 6. �2

67x� � �

43�

7. �x �

32

� � �89� 8. �

3x4� 5� � �

�75� 9. �

x �4

2� � �

x �2

4�

Find the measures of the sides of each triangle.

10. The ratio of the measures of the sides of a triangle is 3:4:6, and its perimeter is 104 feet.

11. The ratio of the measures of the sides of a triangle is 7:9:12, and its perimeter is 84 inches.

12. The ratio of the measures of the sides of a triangle is 6:7:9, and its perimeter is 77 centimeters.

Find the measures of the angles in each triangle.

13. The ratio of the measures of the angles is 4:5:6.

14. The ratio of the measures of the angles is 5:7:8.

15. BRIDGES The span of the Benjamin Franklin suspension bridge in Philadelphia,Pennsylvania, is 1750 feet. A model of the bridge has a span of 42 inches. What is theratio of the span of the model to the span of the actual Benjamin Franklin Bridge?

Practice Proportions

NAME ______________________________________________ DATE ____________ PERIOD _____

6-16-1

Skills PracticeSimilar Polygons

NAME ______________________________________________ DATE ____________ PERIOD _____

6-26-2


Less

on

6-2

Determine whether each pair of figures is similar. Justify your answer.

1. 2.

Each pair of polygons is similar. Write a similarity statement, and find x, themeasure(s) of the indicated side(s), and the scale factor.

3. G�H� 4. S�T� and S�U�

5. W�T� 6. T�S� and S�P�

10

8

x � 2

x � 1

SP

M N

L

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9

103

x � 1

5

P

S

RU V

WT

Q

x � 5

x � 5

9

3

44 S

W

XY

T

U26

14

12 13

B C

DA

13

76 x

G

E H

F

7.5

7.5

7.57.5

Z Y

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3

3

33S R

QP

10.5

6 9

59� 35�A C

B

7

4 659� 35�D F

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Determine whether each pair of triangles is similar. Justify your answer.

1. 2.

ALGEBRA Identify the similar triangles, and find x and the measures of theindicated sides.

3. L�M� and Q�P� 4. N�L� and M�L�

Use the given information to find each measure.

5. If T�S� || Q�R�, TS � 6, PS � x � 7, 6. If E�F� || H�I�, EF � 3, EG � x � 1,QR � 8, and SR � x � 1, HI � 4, and HG � x � 3,find PS and PR. find EG and HG.

INDIRECT MEASUREMENT For Exercises 7 and 8, use the following information.A lighthouse casts a 128-foot shadow. A nearby lamppost that measures 5 feet 3 inches castsan 8-foot shadow.

7. Write a proportion that can be used to determine the height of the lighthouse.

8. What is the height of the lighthouse?

F

GE

H

I

S RP

QT

8

N

J LK

Mx � 5

6x � 2

24

12

18N

P

QL

M

x � 3x � 1

18

16 12.516

14

11

M

L N

S R

T42�

42�

24

1812

16J

A K

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W

Practice Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

6-36-3

Skills PracticeParallel Lines and Proportional Parts

NAME ______________________________________________ DATE ____________ PERIOD _____

6-46-4


Less

on

6-4

1. If JK � 7, KH � 21, and JL � 6, 2. Find x and TV if RU � 8, US � 14,find LI. TV � x � 1 and VS � 17.5.

Determine whether B�C� || D�E�.

3. AD � 15, DB � 12, AE � 10, and EC � 8

4. BD � 9, BA � 27, and CE is one third of EA

5. AE � 30, AC � 45, and AD is twice DB

COORDINATE GEOMETRY For Exercises 6–8, use the following information.Triangle ABC has vertices A(�5, 2), B(1, 8), and C(4, 2). Point Dis the midpoint of A�B� and E is the midpoint of A�C�.

6. Identify the coordinates of D and E.

7. Show that B�C� is parallel to D�E�.

8. Show that DE � �12�BC.

9. Find x and y. 10. Find x and y.

3–2x � 2

x � 3

2y � 1

3y � 52x � 1 3y � 8

y � 5x � 7

x

y

O

A C

B

D

E

C

B

E

D

A

R

U V

T

S

HL

K J

I


Find the perimeter of the given triangle.

1. �DEF, if �ABC � �DEF, AB � 36, 2. �STU, if �STU � �KLM, KL � 12,BC � 20, CA � 40, and DE � 35 LM � 31, MK � 32, and US � 28

Use the given information to find each measure.

3. Find PR if �JKL � �NPR, K�M� is an 4. Find ZY if �STU � �XYZ, U�A� is an altitude of �JKL, P�T� is an altitude of altitude of �STU, Z�B� is an altitude of �NPR, KL � 28, KM � 18, and �XYZ, UT � 8.5, UA � 6, and PT � 15.75. ZB � 11.4.

Find x.

5. 6.

PHOTOGRAPHY For Exercises 7 and 8, use the following information.Francine has a camera in which the distance from the lens to the film is 24 millimeters.

7. If Francine takes a full-length photograph of her friend from a distance of 3 meters andthe height of her friend is 140 centimeters, what will be the height of the image on thefilm? (Hint: Convert to the same unit of measure.)

8. Suppose the height of the image on the film of her friend is 15 millimeters. If Francinetook a full-length shot, what was the distance between the camera and her friend?

x28

20 30402x � 1 25x � 4

YX B

Z

TS A

U

MJ L

K

TN R

P

KS

LT

UMBE

CFD

A

Practice Parts of Similar Triangles

NAME ______________________________________________ DATE ____________ PERIOD _____

6-56-5

Skills PracticeFractals and Self-Similarity

NAME ______________________________________________ DATE ____________ PERIOD _____

6-66-6


Less

on

6-6

Stages 1 and 2 of a fractal known as the Cantor set are shown. To get Stage 2, thesegment in Stage 1 is trisected, and the interior of the middle segment is removed.(The interior of a segment is the segment with its endpoints removed.) Theprocess is repeated for subsequent stages.

1. Draw stages 3 and 4 of the Cantor set.

2. How many segments are there in Stage 3? Stage 4?

3. What happens to the length of the line segments in each stage?

4. The Cantor set is the set of points after infinitely many iterations. Is the Cantor set self-similar?

Find the value of each expression. Then, use that value as the next x in theexpression. Repeat the process three times, and describe your observations.

5. 2x � 3, where x initially equals 5

6. �2x

�, where x initially equals 1

Find the first three iterates of each expression.

7. x2 � 1, where x initially equals 2 8. �1x�, where x initially equals 8

Stage 3

Stage 4

Stage 1

Stage 2

© Glencoe/McGraw-Hill A3 Glencoe Geometry

An

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Skil

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____

____

____

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6-1

6-1

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1.FO

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ALL

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2:3

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wh

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24

Sol

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,and

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,an

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126

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42 f

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15.T

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5:7:

8,an

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40 i

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Th

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16

3.A

RT

Edw

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Hop

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pain

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:4:6

,an

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104

feet

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t

11.T

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is 8

4 in

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.

21 in

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in.,

36 in

.

12.T

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1.5

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Fin

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13.T

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6-1

6-1

Answers (Lesson 6-1)


Skil

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6-2

6-2

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Det

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Tri

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BC

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(0,0

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(�4,

0),a

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C(�

2,4)

.T

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EF

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C.

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6.IN

TER

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DES

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Gra

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draw

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om t

o de

cide

wh

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to p

lace

fu

rnit

ure

.Fin

d th

e di

men

sion

s of

th

eli

vin

g ro

om i

f th

e sc

ale

in t

he

draw

ing

is 1

in

ch �

4.5

feet

.18

ft

by 1

1 ft

3 in

.4

in.

21 – 2 in.

612

40�

40�

x �

1

x �

3A

F

E

D

BC

14

10

x �

6

x �

9

CN

MD

AB

LP

2412

1416

2118

VU

AC

BT

2512

9

14.4

1524

20

15

JM

QRS

PK

LPra

ctic

e (

Ave

rag

e)

Sim

ilar

Po

lyg

on

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-2

6-2



An

swer

s

Skil

ls P

ract

ice

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3

©G

lenc

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cGra

w-H

ill30

9G

lenc

oe G

eom

etry

Lesson 6-3

Det

erm

ine

wh

eth

er e

ach

pai

r of

tri

angl

es i

s si

mil

ar.J

ust

ify

you

r an

swer

.

1.2.

No

;th

e si

des

are

no

t p

rop

ort

ion

al.

yes;

�A

BC

��

PQ

R(o

r �

QP

R);

SS

S S

imila

rity

3.4.

yes;

�S

TU

��

JPM

;ye

s;�

SK

M�

�R

TQ

;S

AS

Sim

ilari

tyA

A S

imila

rity

ALG

EBR

AId

enti

fy t

he

sim

ilar

tri

angl

es,a

nd

fin

d x

and

th

e m

easu

res

of t

he

ind

icat

ed s

ides

.

5.A �

C�an

d E�

D�6.

J�L�an

d L�

M�

�A

BC

��

DB

E;

15;

16;

20�

JKL

��

MN

L;

10;

28;

7

7.E�

H�an

d E�

F�8.

U�T�

and

R�T�

�D

EF

��

GE

H;

4;9;

18�

RS

T�

�U

VT

;12

;6;

14

6

14

S

U

V

RT

x �

4 x �

612

9

6

9

D

E

FH G

x �

5

16

4MN

L

J

K

x �

18

x �

3

1512

D

EC

BAx

� 1

x �

5

30�

60�

RQM

S

K

T

2170

�

15

MJ

P

1470

�10

U

S

T

12

128

9

96

CP

QR

A

B

2014

1312

219 S

WX

Y

R

T

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lenc

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cGra

w-H

ill31

0G

lenc

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eom

etry

Det

erm

ine

wh

eth

er e

ach

pai

r of

tri

angl

es i

s si

mil

ar.J

ust

ify

you

r an

swer

.

1.2.

yes;

�JA

K�

�W

SY

;N

o;

the

sid

es a

re n

ot

pro

po

rtio

nal

.S

AS

Sim

ilari

ty

ALG

EBR

AId

enti

fy t

he

sim

ilar

tri

angl

es,a

nd

fin

d x

and

th

e m

easu

res

of t

he

ind

icat

ed s

ides

.

3.L �

M�an

d Q�

P�4.

N�L�

and

M�L�

�L

MN

��

PQ

N;

9;12

;8

�JL

N�

�K

LM

;2;

21;

14

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

5.If

T�S�

|| Q�R�

,TS

�6,

PS

�x

�7,

6.If

E�F�

|| H�I�,

EF

�3,

EG

�x

�1,

QR

�8,

and

SR

�x

�1,

HI

�4,

and

HG

�x

�3,

fin

d P

San

d P

R.

fin

d E

Gan

d H

G.

PS

�12

;P

R�

16E

G�

6;H

G�

8

IND

IREC

T M

EASU

REM

ENT

For

Exe

rcis

es 7

an

d 8

,use

th

e fo

llow

ing

info

rmat

ion

.A

lig

hth

ouse

cas

ts a

128

-foo

t sh

adow

.A n

earb

y la

mpp

ost

that

mea

sure

s 5

feet

3 i

nch

es c

asts

an 8

-foo

t sh

adow

.

7.W

rite

a p

ropo

rtio

n t

hat

can

be

use

d to

det

erm

ine

the

hei

ght

of t

he

ligh

thou

se.

Sam

ple

an

swer

:If

x�

hei

gh

t o

f lig

hth

ou

se,�

5.x 25�

��12 88 �

.

8.W

hat

is

the

hei

ght

of t

he

ligh

thou

se?

84 f

t

F

GE

H

I

SR

P

QT

8N

JL

K

Mx

� 5

6x �

2

24

12

18N

P

QL

M

x �

3x

� 1

18

1612

.516

14

11

M

LN

SR

T42

�

42�

24

1812

16J

AK

YS

W

Pra

ctic

e (

Ave

rag

e)

Sim

ilar T

rian

gle

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-3

6-3



Skil

ls P

ract

ice

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4

©G

lenc

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cGra

w-H

ill31

5G

lenc

oe G

eom

etry

Lesson 6-4

1.If

JK

�7,

KH

�21

,an

d J

L�

6,2.

Fin

d x

and

TV

if R

U�

8,U

S�

14,

fin

d L

I.T

V�

x�

1 an

d V

S�

17.5

.

1811

;10

Det

erm

ine

wh

eth

er B�

C�|| D�

E�.

3.A

D�

15,D

B�

12,A

E�

10,a

nd

EC

�8

yes

4.B

D�

9,B

A�

27,a

nd

CE

is o

ne

thir

d of

EA

no

5.A

E�

30,A

C�

45,a

nd

AD

is t

wic

e D

B

yes

CO

OR

DIN

ATE

GEO

MET

RYF

or E

xerc

ises

6–8

,use

th

e fo

llow

ing

info

rmat

ion

.T

rian

gle

AB

Ch

as v

erti

ces

A(�

5,2)

,B(1

,8),

and

C(4

,2).

Poi

nt

Dis

th

e m

idpo

int

of A �

B�an

d E

is t

he

mid

poin

t of

A�C�

.

6.Id

enti

fy t

he

coor

din

ates

of

Dan

d E

.

D(�

2,5)

;E

(�0.

5,2)

7.S

how

th

at B�

C�is

par

alle

l to

D�E�

.

Sin

ce t

he

slo

pe

of

B�C�

is �

2 an

d t

he

slo

pe

of

D�E�

is �

2,B�

C�is

par

alle

l to

D�E�.

8.S

how

th

at D

E�

�1 2� BC

.

Th

e le

ng

th o

f D�

E�is

�11

.25

�o

r an

d t

he

len

gth

of

B�C�

is �

45�.

9.F

ind

xan

d y.

10.F

ind

xan

d y.

x�

6,y

�6.

5x

�2,

y�

4

3 – 2x �

2

x �

3

2 y �

1

3y �

52x

� 1

3 y �

8y

� 5

x �

7

�45�

�2

x

y

O

AC

B

D

E

CB

ED

A

R

UV

T

S

HL

KJ

I

©G

lenc

oe/M

cGra

w-H

ill31

6G

lenc

oe G

eom

etry

1.If

AD

�24

,DB

�27

,an

d E

B�

18,

2.F

ind

x,Q

T,a

nd

TR

if Q

T�

x�

6,fi

nd

CE

.S

R�

12,P

S�

27,a

nd

TR

�x

�4.

1612

;18

;8

Det

erm

ine

wh

eth

er J�

K�|| N�

M�.

3.J

N�

18,J

L�

30,K

M�

21,a

nd

ML

�35

no

4.K

M�

24,K

L�

44,a

nd

NL

��5 6� J

N

yes

CO

OR

DIN

ATE

GEO

MET

RYF

or E

xerc

ises

5 a

nd

6,u

se t

he

foll

owin

g in

form

atio

n.

Tri

angl

e E

FG

has

ver

tice

s E

(�4,

�1)

,F(2

,5),

and

G(2

,�1)

.Poi

nt

Kis

th

e m

idpo

int

of E �

G�an

d H

is t

he

mid

poin

t of

F�G�

.

5.S

how

th

at E�

F�is

par

alle

l to

K�H�

.

Th

e sl

op

e o

f E�

F�is

1 a

nd

th

e sl

op

e o

f K�

H�is

1,

so E�

F�is

par

alle

l to

K�H�

.

6.S

how

th

at K

H�

�1 2� EF

.

Th

e le

ng

th o

f K�

H�is

3�

2�,an

d t

he

len

gth

of

E�F�

is 6

�2�.

7.F

ind

xan

d y.

8.F

ind

xan

d y.

x�

4,y

�9

x�

�5 2� ,y

��9 4�

9.M

APS

Th

e di

stan

ce f

rom

Wil

min

gton

to

Ash

Gro

ve a

lon

g K

enda

ll i

s 82

0 fe

et a

nd

alon

g M

agn

olia

,660

fee

t.If

th

e di

stan

ce b

etw

een

Bee

ch a

nd

Ash

Gro

ve a

lon

g M

agn

olia

is

280

feet

,wh

at i

s th

e di

stan

ce b

etw

een

th

e tw

o st

reet

s al

ong

Ken

dall

?

abo

ut

348

ft

Ash

Grov

e

Beec

h

Mag

nolia

Kend

all

Wilm

ingt

on

4 – 3y �

2

3 x �

4x

� 1

4 y �

43x

� 4

2 – 3y �

31 – 3y

� 6

5 – 4x �

3

x

y

O

EGF H

K

NL

J

KM

S

Q

TR

P

D

EC BA

Pra

ctic

e (

Ave

rag

e)

Par

alle

l Lin

es a

nd

Pro

po

rtio

nal

Par

ts

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-4

6-4



An

swer

s

Skil

ls P

ract

ice

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-5

6-5

©G

lenc

oe/M

cGra

w-H

ill32

1G

lenc

oe G

eom

etry

Lesson 6-5

Fin

d t

he

per

imet

er o

f th

e gi

ven

tri

angl

e.

1.�

JK

L,i

f �

JK

L�

�R

ST

,RS

�14

,2.

�D

EF

,if

�D

EF

��

AB

C,A

B�

27,

ST

�12

,TR

�10

,an

d L

J�

14B

C�

16,C

A�

25,a

nd

FD

�15

50.4

40.8

3.�

PQ

R,i

f �

PQ

R�

�L

MN

,LM

�16

,4.

�K

LM

,if

�K

LM

��

FG

H,F

G�

30,

MN

�14

,NL

�27

,an

d R

P�

18G

H�

38,H

F�

38,a

nd

KL

�24

3884

.8

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

5.F

ind

FG

if �

RS

T�

�E

FG

,S�H�

is a

n

6.F

ind

MN

if �

AB

C�

�M

NP,

A�D�

is a

n

alti

tude

of

�R

ST

,F �J�

is a

n a

ltit

ude

of

alti

tude

of

�A

BC

,M�Q�

is a

n a

ltit

ude

of

�E

FG

,ST

�6,

SH

�5,

and

FJ

�7.

�M

NP

,AB

�24

,AD

�14

,and

MQ

�10

.5.

8.4

18

Fin

d x

.

7.�

HK

L�

�X

YZ

8.

8�1 3�

8.4

LH

K

18

10

Y

15

x

ZX

7

20

24

x

C

A

BD

PN

QM

JG

E

F

HT

R

S

GL K

M

F

H

LM

PQ

RN

A

BC

D

EF

RS

T

JK

L

©G

lenc

oe/M

cGra

w-H

ill32

2G

lenc

oe G

eom

etry

Fin

d t

he

per

imet

er o

f th

e gi

ven

tri

angl

e.

1.�

DE

F,i

f �

AB

C�

�D

EF

,AB

�36

,2.

�S

TU

,if

�S

TU

��

KL

M,K

L�

12,

BC

�20

,CA

�40

,an

d D

E�

35L

M�

31,M

K�

32,a

nd

US

�28

93.3�

65.6

25

Use

th

e gi

ven

in

form

atio

n t

o fi

nd

eac

h m

easu

re.

3.F

ind

PR

if �

JK

L�

�N

PR

,K�M�

is a

n

4.F

ind

ZY

if �

ST

U�

�X

YZ

,U�A�

is a

n

alti

tude

of

�J

KL

,P �T�

is a

n a

ltit

ude

of

alti

tude

of

�S

TU

,Z�B�

is a

n a

ltit

ude

of

�N

PR

,KL

�28

,KM

�18

,an

d �

XY

Z,U

T�

8.5,

UA

�6,

and

PT

�15

.75.

ZB

�11

.4.

24.5

16.1

5

Fin

d x

.

5.6.

13.5

16.8

PHO

TOG

RA

PHY

For

Exe

rcis

es 7

an

d 8

,use

th

e fo

llow

ing

info

rmat

ion

.F

ran

cin

e h

as a

cam

era

in w

hic

h t

he

dist

ance

fro

m t

he

len

s to

th

e fi

lm i

s 24

mil

lim

eter

s.

7.If

Fra

nci

ne

take

s a

full

-len

gth

ph

otog

raph

of

her

fri

end

from

a d

ista

nce

of

3 m

eter

s an

dth

e h

eigh

t of

her

fri

end

is 1

40 c

enti

met

ers,

wh

at w

ill

be t

he

hei

ght

of t

he

imag

e on

th

efi

lm?

(Hin

t:C

onve

rt t

o th

e sa

me

un

it o

f m

easu

re.)

11.2

mm

8.S

upp

ose

the

hei

ght

of t

he

imag

e on

th

e fi

lm o

f h

er f

rien

d is

15

mil

lim

eter

s.If

Fra

nci

ne

took

a f

ull

-len

gth

sh

ot,w

hat

was

th

e di

stan

ce b

etw

een

th

e ca

mer

a an

d h

er f

rien

d?2.

24 m

x28

2030

402x

� 1

25x

� 4

YX

BZ

TS

AU

MJ

L

K

TN

R

P

KS

LT

UM

B E

CF

DA

Pra

ctic

e (

Ave

rag

e)

Par

ts o

f S

imila

r Tri

ang

les

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-5

6-5



Skil

ls P

ract

ice

Fra

ctal

s an

d S

elf-

Sim

ilari

ty

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

6-6

6-6

©G

lenc

oe/M

cGra

w-H

ill32

7G

lenc

oe G

eom

etry

Lesson 6-6

Sta

ges

1 an

d 2

of

a fr

acta

l k

now

n a

s th

e C

anto

r se

t ar

e sh

own

.To

get

Sta

ge 2

,th

ese

gmen

t in

Sta

ge 1

is

tris

ecte

d,a

nd

th

e in

teri

or o

f th

e m

idd

le s

egm

ent

is r

emov

ed.

(Th

e in

teri

or o

f a

segm

ent

is t

he

segm

ent

wit

h i

ts e

nd

poi

nts

rem

oved

.) T

he

pro

cess

is

rep

eate

d f

or s

ub

seq

uen

t st

ages

.

1.D

raw

sta

ges

3 an

d 4

of t

he

Can

tor

set.

2.H

ow m

any

segm

ents

are

th

ere

in S

tage

3?

Sta

ge 4

?

4 se

gm

ents

;8

seg

men

ts

3.W

hat

hap

pen

s to

th

e le

ngt

h o

f th

e li

ne

segm

ents

in

eac

h s

tage

?

Th

e lin

e se

gm

ents

dec

reas

e in

len

gth

by

two

-th

ird

s at

eac

h s

tag

e.

4.T

he

Can

tor

set

is t

he

set

of p

oin

ts a

fter

in

fin

itel

y m

any

iter

atio

ns.

Is t

he

Can

tor

set

self

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6-6

6-6


chapter 6 resource masters...stages 1 and 2 of a fractal known as the cantor set are shown. to get...

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