Kumpulan Soal Kongruen Kesebangunan

8/18/2019 Kumpulan Soal Kongruen Kesebangunan

1/14

A

B C

D E

2 c m

3 c m

4 c m

AB

C

D3 2 c m8 c m

4 0 m

6 0 m

P Q

RS

A

B

1 4 c m8 c m

5 c mx c m

Latihan Soal Kelas I! Kesebangunan dan Kekongruenan

1" Pasan#an $an#%n &ata' $e'i(%t )an# *asti se$an#%n a&alah +"A" D%a se#iti#a sama (a(iB" D%a ,a,a'an #en,an#C" D%a $elah (et%*atD" D%a se#iti#a sama sisi

2" -i(a &%a $%ah t'a*esi%m *a&a #am$a' &i sam*in#

se$an#%n. ma(a nilai / a&alah +"A" 22.4B" 8.5C" 2.86D" 5.5

3" Pan,an# $a)an#an *ohon oleh sina' mataha'i a&alah 15 m" Pa&a tem*at &an saat )an# sama tian# $en&e'a se*an,an# 3

m memili(i *an,an# $a)an#an 6 m" in##i *ohon a&alah +"A" 6 mB" .5 mC" 8.5 mD" m

4" Pa&a la)a' teleisi *an,an# se$%ah mo$il a&alah 14 cm &an tin##in)a 4 cm" -i(a tin##i se$ena'n)a a&alah 1 m. ma(a *an,an# mo$il se$ena'n)a a&alah +"A" 3 mB" 3.5 mC" 4 mD" 4.5 m

5" Pe'hati(an #am$a' &i sam*in# Se#iti#a ABC si(%si(% &i B" -i(a

AD 3 cm. DB 2 cm &an BC 4 cm. ma(a *an,an# D7 a&alah

+"A" 2.4 cmB" 6. cmC" 3.5 cmD"

3.6 cm

6" Pe'hati(an #am$a' &i sam*in# Se#iti#a ACB si(%si(% &i titi( C"

-i(a *an,an# AD 32 cm &an DB 8 cm. ma(a *an,an# CD

a&alah +"A" 4 cmB" 8 cmC" 16 cmD" 32 cm

" Pa&a masin#masin# sisi lahan $e'%(%'an 60 m 40 m× a(an&i$%at ,alan se*e'ti #am$a' &i sam*in#" -i(a sisi (anan. (i'i &an

atas a(an &i$%at ,alan sele$a' 6 m. ma(a le$a' ,alan $a#ian $aaha&alah +"A" 12 mB" 10 mC" mD" 8 m

8" Pe'hati(an *e'se#i *an,an# &i sam*in# Bi&an# ABSP &an PQRS

se$an#%n" -i(a *an,an# PQ 16 cm &an QR 12 cm. ma(a

*an,an# BS a&alah +"

1


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P

Q R

A

BC

6 c m

8 c m

4 c m

A B

CD

7 9

4 c m

6 c m

5 c m

1 5 c m

2 c m

6 c m

4 c m

A B

C

D

7

A

B C

P

Q R

A

B

C

D

:

A

B C

R Q

P2 8 O

/

)1 1 8

O


A" .2 cmB" 8 cmC" cmD" 10 cm

" Pe'hati(an &%a se#iti#a ABC &an PQR &i sam*in#

-i(a se#iti#a ABC &an PQR se$an#%n. ma(a *an,an# AB a&alah +"A" 2 cmB" 3 cmC" 4 cmD" 5 cm

10" Pa&a #am$a' &i sam*in# *an,an# 79 a&alah +A" 4 cmB" 5 cmC" 6 cmD" 8 cm

11" Pe'hati(an se#iti#a &i sam*in#

-i(a AC7 BD7.∠ = ∠ ma(a *an,an# C7a&alah +"A" 6 cm

B" 8 cm

C" 10 cm

D" 12 cm

12" Pe'hati(an se#iti#a ABC &an PQR &i sam*in#

-i(a ABC PQR ∆ ∆: &an oBAC 45 .∠ = ma(a

PQR ∠ = +"A" 60o B" 45o C" 6.5o D" 30o

13" Pe'hati(an #am$a' &i sam*in#Pan,an# AB 12 cm. CD 8 cm &an AC 24 cm"

-i(a AB: CD:.∆ ∆: ma(a *an,an# :C a&alah +"A" 16 cmB" 4 cmC" 8 cmD" .6 cm

14" Di(etah%i se#iti#a ABC &an PQR se$an#%n"

-i(a oC 28∠ = &anoQ 118 .∠ = ma(a nilai

/ )− = +"A" 6o B" 4o C" o D" 3o

2


3/14

A B

C D

7

;

9

P

Q R

K

L

<

A

BC

D

L

K

<

P

QR

S

=

1 2 c m

4 c m

5 c m

/

A

B C

D

7

9


15" Di(etah%i $an#%n ABC se$an#%n &en#an PQR" -i(a AB 6 cm. BC 8 cm &an PR 10 cm. ma(a *an,an# PQ a&alah

+"A" 6.5 cmB" 4.8 cmC" .5 cmD" 13.3 cm

16" Pe'hati(an ,a,a'an #en,an# &i sam*in#

A7 BC. A9 CD.⊥ ⊥ AB 4 cm. BC 5 cm.&an B7 3 cm. ma(a *an,an# D9 +"

A" 3.65 cm

B" 3.5 cm

C" 3.6 cmD" 11. 25 cm

1" Di(etah%i *e'se#i *an,an# ABCD &en#an *an,an# 8 cm &an le$a' 6 cm

se*e'ti #am$a' &i sam*in#" -i(a 1A7 AD.2

= ma(a *an,an# 9; a&alah

+"A" 6.5 cmB" 4.6 cmC" .5 cmD" 8.5 cm

18" -i(a *an,an# KP 20 cm. K< 10 cm &an Q< 8 cm.ma(a *an,an# LP a&alah +"A" 16 cmB" 12 cmC" 10 cmD"

4 cm

1" Di(etah%i *an,an# CD 8 cm. AK 5 cm &an LC 4.8 cm"Pan,an#


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P Q

RS

< >

P

QR

K L

A

B

C

D

7

a $

c

A

B CD

e

?

7


22" Pa&a #am$a' &i sam*in#. *an,an# PQ 40 cm.=

S< 10 cm= &an


5/14

A

B C

D

S

A B

C

K

L


6/14

A B

CD

:


Pe'hati(an ,a,a'an #en,an# ABCD"

• ABD CDB. ADB CBD. BAD BCD∠ = ∠ ∠ = ∠ ∠ = ∠

• AB CD. AD BC= =

-a&i ABD CDB∆ ≅ ∆

30" Pe'hati(an *e'se#i *an,an# ABCD &i sam*in# -i(a titi( : a&alah titi(

ten#ah sisi AB. ma(a &%a $an#%n )an# (on#'%en a&alah +"A" AD: &an CD:B" BC: &an CD:C" AD: &an BC:D" BC: &an ABCD

-aa$an ! C

Pem$ahasan !Pe'hati(an $an#%n ABCD"

• AB CD= &an AD BC=

• A B C D∠ = ∠ = ∠ = ∠

iti( : a&alah titi( ten#ah AB. ma(a!• A: B:= &an A: B:=

• AD: BC:∠ = ∠ &an A:D B:C∠ = ∠-a&i AD: BC:"≅

31" Si?at (e(on#'%enan se#iti#a $e'i(%t $ena'. kecuali+"A" Simet'isB" Re?le(ti? C" 'ansiti? D" Dilatasi

-aa$an ! D

Pem$ahasan!Ke(on#'%enan se#iti#a memili(i si?at 'e?le(ti?. simet'is &an t'ansiti?"

33" Pe'hati(an #am$a' &i sam*in# -i(a ABD;

$elah (et%*at. ma(a *asan#an se#iti#a )an#(on#'%en a&alah +"7" AB∆ &an D79∆9" D79∆ &an BC∆;" AB∆ &an A9;∆" A9C∆ &an ABC∆

Pembahasan!

Ka'ena ABD; $elah (et%*at. ma(a

AB BD D; A;= = = &an A;9 AB"∠ = ∠

Pe'hati(an $ahaoAB 0 AB∠ = ∠ &an o;A9 0 5 A;9∠ = ∠ "

Ka'ena A;9 AB.∠ = ∠ ma(a A9; AB"∠ = ∠

Ka'ena AB A;.= A;9 AB∠ = ∠ &an A9; AB.∠ = ∠ ma(a $e'&asa'(an &alil s%&%tsisis%&%t &i*e'oleh

A;9 AB"∆ ≅ ∆

Jawaban! C

6


7/14

P

Q

R

S

A

B

CD

7


32" Pa&a #am$a' &i sam*in#. ABC CD7"∆ ≅ ∆ -i(aAC 15 cm &an D7 cm. ma(a l%as $an#%n ABCD7

a&alah + cm2

A" 0B" 180

C" 12D" 80

-aa$an ! BPem$ahasan!

Ka'ena ABC CD7.∆ ≅ ∆ ma(a AB D7 = = cm &an

L%as ABC∆ L%as CD7"∆

Pe'hati(an ABC.∆

2 2 2 2BC AC AB 15 12= − = − = cm"

L%as21 1ABC AB BC 15 12 0 cm

2 2∆ = × × = × × =

L%as $an#%n ABCD72L%as ABC L%as CD7 180 cm "= ∆ + ∆ =

33" Ban#%n la)an#la)an# &i sam*in# &i$ent%( &a'i &%ase#iti#a )an# (on#'%en. )ait% se#iti#a PSR &an se#iti#a

PQR" -i(a SQ 12 cm= &an R 8 cm.= ma(a *an,an#(elilin# la)an#la)an# a&alah +"A" 4.5 cmB" .5 cmC" 25 cmD" 35 cm

-aa$an ! D

Pem$ahasan!

Ka'ena ABC CD7.∆ ≅ ∆ ma(a

• S Q 6 cm"= = • RS RQ. SP PQ= =

Pan&an# PRS.∆

Pe'hati(an $aha RS SP.∆ ∆:

S R

P S=

6 8

P 6⇒ =

6 6P 4.5

8

×⇒ = = cm"

Pe'hati(an $aha PRS PS.∆ ∆:

•PR PS

PS P=

12.5 PSPS 12.5 4.5 .5 cm"

PS 4.5⇒ = ⇒ = × =

• PR RSPS S

= 12.5 RS 12.5 6RS 10 cm".5 6 .5

×⇒ = ⇒ = =


8/14

A B

C

D

7

9

A

B

C

D

K

L


A" 2 cmB" 3 cmC" 4 cmD" 5 cm-aa$an! D

Pem$ahasan!

Ka'ena ABC 7DC.∆ ≅ ∆

ma(a• AB 7D 4 cm= =

• AC CD=

Ka'ena AD 10 cm= &an AC CD.= ma(a1

AC AD 52

= = cm"

Sehin##a

2 2 2 2BC AC AB 5 4 3 cm"= − = − =

35" Pe'hati(an #am$a' &i sam*in#"

Di(etah%i *an,an# BC D7 cm. D9 15 cm

&an AC 10= cm" Pan,an# A7 +"A" 12 cmB" 3 cmC" 24 cmD" 2 cm-aa$an! B

Pem$ahasan!

Ka'ena BC D7 cm. o7 B 0∠ = ∠ = &an D97 C9B.∠ = ∠ ma(a D79 CB9"∆ ≅ ∆

Ka'ena D79 CB9.∆ ≅ ∆ ma(a 79 9B= &an D9 9C 15 cm"= =

Pe'hati(an CB9.∆

2 2 2 29B 9C BC 15 12 cm"= − = − =

Ka'ena 79 9B.= ma(a 7B 79 9B 24 cm"= + =Pe'hati(an ABC.∆

( ) 2

2 2 2AB AC BC 10 2 cm"= − = − =


9/14

AB

C

D

7

P=

R

Q

S


Ka'ena ADC KLC.∆ : ma(a

AD AC

KL KC=

AD 12

4 6⇒ =

4 12AD 8 cm"

6

×⇒ = =

3" Pa&a #am$a' &i sam*in#. &i(etah%i PQ PR. P= 8 cm

&an R= 6 cm" Pan,an# SR +"A" 2 cmB" 3 cmC" 3.5 cmD" 4 cm

-aa$an! DPem$ahasan!

Pan&an# P=R.∆

2 2 2 2PR P= R= 8 6 10 cm"= + = + =

PQ PR 10 cm"

Ka'ena PSQ P=R.∆ ∆ ma(a

PQ SQPR R=

= SQ1 SQ 6 cm6

⇒ = ⇒ =

Ka'ena PQ PR. R= SQ. ma(a P= PS 6 cm

-a&i PSQ P=R"∆ ≅ ∆


10/14


Ban#%n ABCD &an PQRS se$an#%n" Di(etah%i AB 28 cm. CD 4 cm. AD 12 cm. PQ cm. QR

3 cm" Pan,an# SR a&alah +++++++"

a" 5 cm c" 3 cm $" 4 cm &" 1 cm

3" Pe'hati(an #am$a' $e'i(%t

D%a se#iti#a &i atas se$an#%n. ma(a $esas' $e't%'%tt%'%t a&alah +++++a" 600 &an 00 c" 500 &an 800

$" 00 &an 400 &" 800 &an 400


Pa&a #am$a' &i atas. . *an,an# AC +++++++"

a" cm c" 12 cm

10

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11/14


$" 10 cm &" 24 cm

5" Di(etah%i se#iti#a ABC &an se#iti#a DEF se$an#%n" Pan,an# sisi AC 16 cm. BC 18 cm. &an DE

24 cm" Pan,an# AB +++++++"

a" cm c" 12 cm

$"

10 cm &" 15 cm

6" Pan,an# AD *a&a #am$a' &i $aah ini a&alah """""""""

a" 48 cm c" 10 cm

$" 5 cm &" 12 cm

" Pa&a #am$a' &i $aah ini *an,an# ED = """""""""""""""""""""

a" 3 cm $" 4 cm c" 13 cm &" 12 cm


11

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12/14


Pan,an# KL +++++++"

a" 3 cm c" 15 cm

$" cm &" 16 cm

" in##i *ohon *isan# a&alh 3 mete' &an *an,an# $a)an#ann)a 2 m" *a&a saat )an# sama *an,an#

$a)an#an se$%ah tian# $en&e'a a&alah 6 m" tin##i tian# $en&e'a a&alah +++

a" 10 m c" 6 m $" m &" 4 m

10" Pa&a #am$a' &i sam*in#. AD AF

ABEH a&alah $elah (et%*at" Pasan#anse#iti#a $e'i(%t )an# (on#'%en

a&alah +++++++"

a"

$"

c"

&"

11" Se$%ah ?oto $e'%(%'an le$a' cm &an *an,an#n)a 12 cm a(an &i*asan# *a&a se$%ah $in#(ai )an# *an,an#n)a 20 cm" Le$a' $in#(ai ?oto. a#a' ?oto an $in#(ai se$an#%n a&alah +++""

a" 18 cm c" 15 cm $" 16 cm &" 14 cm12" Se$%ah *ohon tin##in)a 24 m &an tian# $en&e'a 8 m" -i(a $a)an#an *ohon 15 m ma(a $a)an#an tian#

$en&e'a a&alah +++++++"

a" 4 m c" 6 m $" 5 m &" 8 m

12

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13/14


13" Pa&a . AB 15 cm. BC cm &an AC 12 cm &an *a&a s#iti#a PQR . QR 6 cm. PQ 8

cm. PR 10 cm"


14/14


1" Seo'an# ana( tin##in)a 1.60 cm *a&a s%at% so'e $a)an#ann)a 2 m" Se$atan# *ohon *an,an#

$a)an#ann)a *a&a saat )an# sama 15 m. ma(a tin##i *ohon it% a&alah +++++""a" 8 m c" 12 m

$" 10.6 m &" 18.5 m

20" . &en#an AB 12 cm. BC 6 cm &an CE 10 cm. ma(a *an,an# DE a&alah++++""

a" cm c" 13 cm

$" 10 cm &" 15 cm

14
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Kumpulan Soal Kongruen Kesebangunan