+" A" B" C" D"
<
25 cm 30 cm 34 cm 38.4 cm
Q
P
P
23" Pa&a #am$a' &i sam*in#. *an,an# PL = 12 cm. LQ = 8 cm &an QR = 30 cm" Pan,an# LK a&alah + A" 12 cm B" 18 cm C" 20 cm D" 45 cm
=
AC
⇒
8
=
4
⇒
C7 =
CD C7 10 C7 A7 = AC + C7 = 4 + 5 = cm"
10 × 4 8
R
B" C" D"
e ? e ? e ? e ?
=
a+$
=
e =
a+$
7
C A D
= 5 cm"
a =
a+$ c+& c
7
c+ & c+ & c
=
$ =
A e
? =
Q
B
25" Pe'hati(an #am$a' &i sam*in# Pe'n)ataan )an# $ena' a&alah +" A"
L
K
24" Pa&a #am$a' &i sam*in#. AB @ @D7" -i(a AC 4 cm. BC 8 cm &an CD 10 cm. ma(a *an,an# A7 a&alah +" A" 5 cm B" .2 cm C" cm D" 10 cm -aa$an! C Pe'hati(an $aha ∆ABC : ∆7DC"
BC
>
c
? B
a
D
$
C
c+ & &
=
a+$ $
-aa$an ! D Pem$ahasan! Pe'hati(an $aha ∆ABC ∆7DC"
4
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
AB
=
7D
AC 7C
=
BC
⇒
DC
e
=
c+&
?
=
a+$
c
$
26" Pe'hati(an #am$a' &i sam*in# -i(a ∆ABC ≅ ∆KL<. ma(a *e'n)ataan )an# $ena' a&alah + A" c 2 = ( 2 + $ 2 2
2
B" c = ( − $
L C K (
$
2
C" ( 2 = $ 2 − c 2 D" c 2 = $ 2 − ( 2 -aa$an ! B Pem$ahasan! Ka'ena ∆ABC ≅ ∆KL<. ma(a BC = L< = ("
B
c
A
<
Pe'hati(an ∆ABC"
BC2
=
AC2 + AB2
⇒
(2
=
$ 2 + c2
2
⇒c =
$ 2 − ( 2
2" -i(a ∆ABC ≅ ∆79;. ma(a (o'es*on&ensi )an# $ena' a&alah +" A" B"
∠A = ∠7 &an AC = 9; ∠A = ∠9 &an
A9 = 9;
C" ∠B = ∠9 &an BC = 9; D" ∠B = ∠; &an AB = 79 -aa$an! C Pem$ahasan! Ka'ena ∆ABC ≅ ∆79;. ma(a •
∠A = ∠7. ∠ B = ∠9. ∠C = ∠ ;
•
AB = 79. BC = 9;. AC = 7;
28" Salah sat% &alil )an# &a*at &i#%na(an %nt%( mem$%(ti(an &%a se#iti#a )an# (on#'%en a&alah +" A" s%&%t. s%&%t. s%&%t B" s%&%t. sisi. s%&%t C" sisi. sisi. s%&%t D" s%&%t. s%&%t. sisi -aa$an! B Pem$ahasan! Dalil )an# &i#%na(an %nt%( mem$%(ti(an &%a se#iti#a )an# (on#'%en a&alah! s%&%t. sisi. s%&%t • sisi. s%&%t. sisi • • sisi. sisi. sisi 2" Pasan#an se#iti#a )an# (on#'%en &a'i ,a,a'an #en,an# ABCD a&alah +" A" ∆ADS &an ∆SDC B" C"
A
D S
∆ADS &an ∆ABS
∆ABD &an ∆CDB
D" ∆ABD &an ∆ABC -aa$an! C Pem$ahasan!
B
C
5
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
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 $an#%n )an# (on#'%en a&alah +" A" AD: &an CD: B" BC: &an CD: C" AD: &an BC: D" BC: &an ABCD
A
D
:
B
C
-aa$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 $ena'. kecuali+" A" Simet'is B" Re?le(ti? C" 'ansiti? D" Dilatasi -aa$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 $aha ∠AB = 0
o
∠AB &an
∠;A9 = 0
o
5 ∠A;9 "
Ka'ena ∠A;9 = ∠AB. ma(a ∠A9; = ∠AB" Ka'ena AB = A;. ∠A;9 = ∠AB &an ∠A9; = ∠AB. ma(a $e'&asa'(an &alil s%&%tsisis%&%t &i*e'oleh ∆A;9 ≅ ∆AB" Jawaban!
C
6
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
32" Pa&a #am$a' &i sam*in#. ∆ABC ≅ ∆CD7" -i(a AC 15 cm &an D7 cm. ma(a l%as $an#%n ABCD7 a&alah + cm2 A" 0 B" 180 C" 12 D" 80 -aa$an ! B Pem$ahasan! Ka'ena ∆ABC ≅ ∆CD7. ma(a AB = D7 = cm &an L%as ∆ABC L%as ∆CD7" Pe'hati(an ∆ABC.
BC = AC2 − AB2 = 152 − 2 = 12 cm" 1 1 2 L%as ∆ABC = × AB × BC = × 15× 12 = 0 cm 2 2 2 L%as $an#%n ABCD7 = L%as ∆ABC + L%as ∆ CD7 = 180 cm " R
33" Ban#%n la)an#la)an# &i sam*in# &i$ent%( &a'i &%a se#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 cm B" .5 cm C" 25 cm D" 35 cm -aa$an ! D Pem$ahasan! Ka'ena ∆ABC ≅ ∆CD7. ma(a
Q
P
S
S = Q = 6 cm" RS = RQ. SP = PQ • Pan&an# ∆PRS. Pe'hati(an $aha ∆RS : ∆SP. •
S
=
P
R
⇒
S
6
=
8
P =
6×6
6 8 Pe'hati(an $aha ∆PRS : ∆PS. 12.5 PS PR PS ⇒
=
•
•
P
⇒
PS PR PS
=
P RS S
⇒
=
PS 12.5 .5
=
4.5 RS 6
=
4.5 cm"
⇒
PS = 12. 5× 4. 5 = . 5 cm"
⇒
RS =
12.5 × 6 .5
= 10 cm"
34" Pa&a #am$a' &i sam*in#. &i(etah%i ∆ABC ≅ ∆7DC" -i(a *an,an# 7D = 4 cm &an AD = 10 cm. ma(a Pan,an# BC a&alah +" B C
D
A
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
A"
2 cm 3 cm C" 4 cm D" 5 cm -aa$an! D Pem$ahasan! Ka'ena ∆ABC ≅ ∆7DC. ma(a B"
• •
AB = 7D = 4 cm AC = CD
Ka'ena AD = 10 cm &an AC = CD. ma(a AC =
1 2
AD = 5 cm"
Sehin##a
BC = AC2 − AB2
=
52 − 42
=
3 cm" D
35" Pe'hati(an #am$a' &i sam*in#" Di(etah%i *an,an# BC D7 cm. D9 15 cm
&an AC = 10 cm" Pan,an# A7 +" 9 B A A" 7 12 cm B" 3 cm C" 24 cm D" 2 cm C -aa$an! B Pem$ahasan! Ka'ena BC D7 cm. ∠7 = ∠B = 0o &an ∠D97 = ∠C9B. ma(a ∆D79 ≅ ∆CB9" Ka'ena ∆D79 ≅ ∆CB9. ma(a 79 = 9B &an D9 = 9C = 15 cm" Pe'hati(an ∆CB9.
9B = 9C2 − BC2 = 152 − 2 = 12 cm" Ka'ena 79 = 9B. ma(a 7B = 79 + 9B = 24 cm" Pe'hati(an ∆ABC. AB = AC2 − BC2
=
(
10
)
2
2
− =
2 cm"
A7 = AB − 7B = 2 − 24 = 3 cm" 36" Pa&a #am$a' &i sam*in#. ∆ABC ≅ ∆ADC"
B
-i(a *an,an# AC = 12 cm. KL = 4 cm. KC = 6 cm. AD @ @ KL &an ∠DAC = ∠DAC.
ma(a *an,an# AB a&alah +" A" 8 cm B" 11 cm C" 13 cm D" 16 cm -aa$an! A Pem$ahasan!
K
A
D
C
L
Ka'ena ∆ABC ≅ ∆ADC. ma(a AB = AD" Pan&an# ∆ADC.
8
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
Ka'ena ∆ADC : KLC. ma(a
AD
=
KL
AC
⇒
AD
KC
=
4
12
⇒
6
AD =
4 × 12 6
= 8 cm"
3" Pa&a #am$a' &i sam*in#. &i(etah%i PQ PR. P= 8 cm &an R= 6 cm" Pan,an# SR +" A" 2 cm B" 3 cm C" 3.5 cm D" 4 cm -aa$an! D Pem$ahasan!
R
S
P
Q
=
Pan&an# ∆P=R.
PR = P= 2 + R= 2
=
82 + 6 2
= 10 cm"
PQ PR 10 cm" Ka'ena ∆PSQ ∆P=R. ma(a
PQ
=
PR
SQ R=
⇒1=
SQ 6
⇒ SQ =
6 cm
Ka'ena PQ PR. R= SQ. ma(a P= PS 6 cm -a&i ∆PSQ ≅ ∆ P=R"
SR = PR − PS = 10 − 6 = 4 cm" 38" Pe'hati(an #am$a' &i sam*in# -i(a ∆ABC ≅ DB7. BC = 12 cm &an
CD =
1 3
C
D
DB. ma(a *an,an# D7 a&alah +"
A"
cm 12 cm C" 13 cm D" 15 cm -aa$an! D B"
1"
A
B
7
Be'i(%t ini )an# *asti se$an#%n a&alah !
a" D%a $an#%n *e'se#i *an,an# $" D%a $an#%n $elah (et%*at c" D%a $an#%n *e'se#i &" D%a $an#%n la)an#la)an# 2"
Pe'hati(an #am$a' &i $aah ini
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
Ban#%n ABCD &an PQRS se$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' a" 600 &an 00 c" 500 &an 800 $" 00 &an 400 &" 800 &an 400 4"
$e't%'%tt%'%t a&alah +++++
Pe'hati(an #am$a' $e'i(%t
Pa&a #am$a' &i atas. a" cm
. *an,an# AC +++++++" c" 12 cm
10
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
$" 10 cm
&" 24 cm
5"
Di(etah%i se#iti#a ABC &an se#iti#a DEF se$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 $" 5 cm
c" 10 cm &" 12 cm
" Pa&a #am$a' &i $aah ini *an,an# ED = """"""""""""""""""""" a" 3 cm
8"
$" 4 cm
c" 13 cm
&" 12 cm
Pe'hati(an #am$a' $e'i(%t
11
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
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#an se#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 $" 16 cm &" 14 cm 12" Se$%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
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
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"
a&alah
a" 14" Se#iti#a si(%si(% ABC . si(%si(% &i A &en#an Se#iti#a xy . si(%si(% &i &en#an Pe'n)ataan )an# $ena' %nt%( se#iti#ase#iti#a it% a&alah +++++++" a" $" c" &" 15" Se#iti#ase#iti#a &i $aah ini )an# se$an#%n &en#an se#iti#a )an# *an,an# sisisisin)a 5 cm. 12 cm. 13 cm. a&alah +++++++" a" 3 cm. 4 cm. 5 cm $" 10 cm. 24 cm. 35 cm c" 2.5 cm 6 cm 6.5 cm &" cm 12 cm 15 cm 16" a" $" c" &"
Ban#%n$an#%n )an# *asti se$an#%n a&alah +++++++" D%a $%ah se#iti#a sama (a(i D%a $%ah se#iti#a sama sisi D%a $%ah t'a*esi%m D%a $%ah *e'se#i *an,an#
1" Se#iti#a ABC sama (a(i. &an #a'is CD me'%*a(an #a'is tin##i. ma(a &en#an s)a'at +++++" a" s. s. s c" s&. s. s& $" s. s&. s &" s. s. s& 18" Se$%ah ?oto &item*at(an *a&a (a'ton $e'%(%'an 50 cm / 0 cm. *a&a *osisi sea'ah &en#an (a'ton" Di se$elah (i'i. (anan. &an atas ?oto te'&a*at sisi (a'ton )an# le$a'n)a 5 cm" -i(a ?oto &an (a'ton se$an#%n. ma(a le$a' (a'ton &i $a#ian $aah ?oto a&alah +++++"" a" 5 cm c" 13 cm $" 10 cm &" 18 cm
13
Latihan Soal Kelas I! Kesebangunan dan Kekongruenan
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 $" 10 cm
c" 13 cm &" 15 cm
14