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IV .Plane Geometry
: I T R A
P Lines ,Rays ,and Angles
s d r o
W Pronunciation Indonesian
t n i o
P /pɔɪn t/ Titik e
n i
L / aɪl n / Garis e
n il l a t n o z i r o
H / h, ɒrɪ’zɒn laɪt l n / Garis datar e
n il l a c i t r e
V /'vɜ:tɪk laɪ l n / Garis tegak e
n il e u q il b
O /ə’bl:ik l aɪn / Garis miring e
n il t h g i a r t
S /streɪt laɪn / Garis l urus e
n il d e v r u
C /kɜ: aɪvl n / Garis l engkung l
e ll a r a
P / ærəp lel/ Sejajar e
n il l e ll a r a
P / ærəp lell aɪn / Garis sejajar t
u
C / Λ /k t Memotong t
c e s r e t n
I /,ɪntə'sekt/ Memotong e
n il d e t c e s r e t n
I /,ɪntə'sektɪd laɪn / Garis berpotongan n
o i t c e s r e t n i f o t n i o
P /pɔɪnt əv ,ɪntə' ks ∫n/ e Titikpotong l
a n o g o h t r
O /,ɔ:θə'gənəl / Tegaklurus Perpendicular /pɜ:pən’dɪkjʊlə(r)/ Tegaklurus
t n e m g e s e n i
L / aɪl n 'segmən t/ Ruasgaris t
n i o p d n
E /endpɔɪn t/ Titik ujung y
a
R /reɪ/ Sinar e
l g n
A /'æŋgl/ Sudut x
e t r e
V /vɜ:teks/ Titiksudut s
e c i t r e
V /vɜ:tɪs:iz/ Titiksudut-titiksudut e
l g n a e t u c
A /ə’kju:t 'æŋgl/ Sudut l ancip e
l g n a t h g i
R / aɪr t æ' ŋgl/ Sudut siku-siku e
l g n a e s u t b
O /əbt’ju:s'æŋgl/ Sudut tumpul e
l g n a t h g i a r t
S /streɪt æ' ŋgl/ Sudut lurus e
l g n a l l u
F /fʊ l æ' ŋgl/ Sudut penuh e
l g n a y r a t n e m e l p m o
C /,kɒmplɪ'mentrɪ æ' ŋgl/ Sudut berpenyiku e
l g n a y r a t n e m e l p p u
S /'sΛ lpɪ'mentrɪ æ' ŋgl/ Sudut berpelurus e
l g n a t n e c a j d
A /ə'dƷeɪs ænt ' ŋgl/ Sudut bersebelahan e
l g n a g n i d n o p s e r r o
C /,kɒrɪ' ps ɒnding'æŋgl/ Sudut sehadap e
l g n a e t i s o p p
O /ɒpəzɪt æ' ŋgl/ Sudut bertolakbelakang
e l g n a r o i r e t n i e t a n r e t l
A /ɔ:l'tɜ:nət ɪn'tɪərɪə(r ) æŋgl/
m a l a d t u d u S
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e l g n a r o i r e t x e e t a n r e t lA /ɔ:l'tɜ:nət ɪk' ts ɪərɪə(r ) æ
' ŋgl/
r a u l t u d u S
n a g n a r e b e s r e b Opposite-interior angle /ɒpəzɪt ɪn'tɪərɪə(r )
æ
' ŋgl/ Sudut dalam sepihak Opposite-exterior angle /ɒpəzɪt ɪk' ts ɪərɪə(r )
æ
' ŋgl/ Sudut l uarsepihak
Example:
¬ Linek i sa horizonta l ilne ¬ Linel i savertica l ilne.
¬ Linem i sanob ilque ilne .
¬ Linesk,l ,and marestraightlines ¬ Linen i sacurved ilne.
¬ Line lis para lle lto ilnem.
¬ Lines land mareparalle.l
¬ Lineacuts ilneb .Lineaintersects ilneb .
¬ Linesaand b are intersected ilnes.
¬ I ftwo ilnesi ntersect ,their i ntersectioni s e
h t d e ll a
c point of i ntersection.
¬ Linep is orthogonalto ilneq .
¬ Linep is perpendicularto ilne q.
¬ Linesp and q are orthogonal.
¬ T ow anglesthathavea sumo f90ºarecomplementary.
¬ I fthemeasureo fAngleAi s400andAngleBi s500 ,then wesayAngleA
e r a B e l g n a d n
a complementaryangles.
¬ Twoanglesthathavea sumo f180ºaresupplementary.
¬ I fthemeasureo fAngleAi s1200 andAngleBi s 600 ,thenwesay Angle
e r a B e l g n a d n a
A supplementaryangles.
m l
a b
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¬ Angle3 and angle5 arealternate i nteriorangles.
¬ Angle1 and angle7 arealternate exteriorangles.
¬ Angle1 and angle2 areadjacentangles.
¬ Angle2 and angle6 arecorrespondingangles.
¬ Angle5 and angle7 are oppositeangles.
¬ Angle3 and angle6 are opposite-interiorangles.
¬ Angle1 and angle8 are opposite-exteriorangles.
I T R A
P I :Two Dimensiona lFigures s
d r o
W Pronunciation Indonesian
n o g y l o
P /'pɒlɪgən / Segibanyak e
l g n a i r
T /' atr ɪæŋgl/ Segitiga l
a r e t a li r d a u
Q /,kwɒdrɪ'lætərəl / Segiempat n
o g a t n e
P /'pentəgən / Segiilma n
o g a x e
H /'heksəgən / Segienam n
o g a t p e
H /'heptəgən / Segitujuh n
o g a t c
O /'ɒktəgən / Segidelapan n
o g a n o
N /'nəʊnəgən / Segisemb lian n- ng o / ne ' gən / Seg in
i
S ed / as ɪd/ S iis e
l g n a r o i r e t n
I /ɪn'tɪərɪə( ær ) ŋgl/ Sudut dalam e
l g n a i r t s e l e c s o s
I /aɪsɒsəl:iz' atr ɪæŋgl/ Segitiga samakaki e
l g n a i r t l a r e t a li u q
E / wi,k ɪ'lætərə l' atr ɪæŋgl/ Segitiga samasisi e
l g n a i r t t h g i
R /raɪt ' atr ɪæŋgl/ Segitiga siku-siku e
l g n a i r t e t u c
A /ə'kju:t ' atr ɪæŋgl/ Segitiga l ancip e
l g n a i r t e s u t b
O /əbt’ju ' a:s tr ɪæŋgl/ Segitiga tumpul e
l g n a i r t e n e l a c
S /'skeli:in' atr ɪæŋgl/ Segitiga sembarang x
e p
A /'eɪpeks/ Titikpuncak e
s a
B /beɪs / Alas t
h g i e
H /haɪ /t Tinggi e
l g n a i r t f o a e r
A /'eərɪə əv ' atr ɪæŋgl/ Luassegitiga
1 2
3
4
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P /pəˈrɪmɪtə/ Keililng t
c e s i
B /bʌ ˈɪsɛk t/ Membag iduasama besar Median /ˈmiːdɪən / Garis berat
r o t c e s i b e l g n
A /æŋglb bʌˈɪsɛktə( / r) Garis bagi e
d u t i t l
A /ˈaltɪtjuːd / Garis tinggi m
a r g o l e ll a r a
P /ˌparəˈlɛləgram/ Jajargenjang e
r a u q
S /'skweə/ Persegi e
l g n a t c e
R /ˈrɛk æt ŋgl/ Persegipanjang s
u b m o h
R /ˈrɒmbəs / Belahketupat e
t i
K /kʌɪt / Layang-layang m
u i z e p a r
T /trəˈpiːzɪəm / Trapesiumsiku-siku d
i o z e p a r
T /ˈtrapɪzɔɪd / Trapesium e
l c r i
C /ˈsəːk(əl) / Lingkaran r
e t n e
C /ˈsɛntə/ Titikpusat s
u i d a
R /ˈreɪdɪəs / Jari-jari ii
d a
R /ˈreɪdiʌɪ/ Jari-jari j(amak) e
c n e r e f m u c r i
C /səˈkʌmfərən s/ Keililng ( ilngkaran) d
r o h
C /kɔːd / Tailbusur r
e t e m a i
D /dʌ ˈɪamɪtə/ Diameter c
r
A /ɒːk / Busur t
n e m g e
S /'segmən t/ Tembereng r
o t c e
S /ˈsɛktə/ Juring t
n a c e
S /ˈsiːkən / t Garis memotong ilngkaran t
n e g n a
T /ˈtæŋʒən t/ Garissinggung ilngkaran t
n e g n a t l a n r e t n
I /ɪnˈtəːnə lˈt ŋæ ʒən t/ Garissinggung dalam t
n e g n a t l a n r e t x
E /ɪkˈstəːnəl ˈtæŋʒən t/ Garisinggungl uar
d e b i r c s n
I /ɪnˈskrʌɪb /
k a y n a b i g e s
( ) Termuat (dalam ilngkaran atau
k a y n a b i g e
s )
d e b i r c s m u c r i
C /ˈsəːkəmskrʌɪb / ( ilngkaran )Memuat )
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Examples:
¬ Polygon are two-dimensiona l ifgures which consists o fn points and d
e ll a c e r a h c i h w s e n il t h g i a r t s y b d e t c e n n o c s t n i o p y b r a e
n sides .
¬ Atriangle isathree– sided ifgure .
¬ Isoscelestriangleisa trianglethathas two equa lsides .
¬ Equ liatera ltriangle isatriangle that hasthree equa lsides.
¬ Right-angle triangle (usually called righttriangle)i sa trianglethat s
a
h one rightangle .
¬ Scalenetriangleisa trianglethat hasthree differentsidesor al lof i ts .
h t g n e l t n e r e ff i d e v a h s e d i s
¬ Acutetriangleisa trianglewhich al lof i tsi nterna langlesareacute
. s e l g n a
¬ Obtuse triangleisatrianglethat hasanobtuseangle.
¬ An angle bisector i s a segment which bisects an angle and connects a .
e d i s e t i s o p p o e h t n o t n i o p a d n a x e t r e v
¬ A median (bisector) si a segment that connects a vertex o fthe triangle e
d i s e t i s o p p o e h t f o t n i o p d i m e h t d n
a .
¬ An altitude is a segment from the vertex o fthe triangle perpendicular to e
d i s e t i s o p p o e h t g n i n i a t n o c e n il e h
t .
¬ Aquadr liateralisany 4sided shape.
¬ Apara llelogramhas2 pairs o fparalle lsides. Atrapezoid hasexactly one pair
. s e d i s l e ll a r a p f o
Akite hasexactly two pairso f . s e d i s t n e c a j d a t n e u r g n o c
Atrapeziumhas exactly one pair o f s e l g n a t h g i r o w t d n a s e d i s l e ll a r a
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¬ Circleistheset o fal lpointsi n aplanethat are agivendistancef romthe .
r e t n e c
¬ Radius(plural :radii) i sa ilne segment that j oins thecenter toa point on .
e l c r i c e h t
c r i C a f o s t r a
P l e
Chord :a ilne j oiningtwo pointson .e l c r i c a
– ACand ABarechords.
Diameter :achord that passes . r e t n e c s e l c r i c e h t h g u o r h t– ACi sa diameter
Arc :two pointson acircle and al l t c e n n o c o t d e d e e n s t n i o p e h t. m e h t
– minor arcABor
– major arcACBor
Centra lAngle :an anglewhose e l c r i c e h t f o r e t n e c e h t t a s i x e t r e v
Sector: I t i saregion enclosed by . e l c r i c e h t f o c r a d n a i i d a r o w tA
B
C
.
O
A
B
C
Arectangleisa parallelogram with 4 .
s e l g n a t h g i r
Arhombusisa parallelogram with 4 h
t g n e l l a u q e f o s e d i s
Asquare isaparallelogramwith4 right . h t g n e l l a u q e f o s e d i s 4 d n a s e l g n a
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Segment:I t i sa region enclosed by e h t g n i n i o j c r a e h t d n a d r o h c ay m e d a m t n e m g e s e h T . d r o h c
e m g e s r o n i m d e ll a c s i c r a r o n i
m nt
s a c r a r o j a m y b t n e m g e s d n a
t n e m g e s r o j a
m .
e l c r i C e h t s t u C t a h t e n i L
Secant :a ilnethat i ntersectsa s t n i o p o w t y l t c a x e t a e l c r i c
Tangent: a ilnethati ntersectsa tn i o p e n o y l t c a x e t a e l c r i c
–
The point o fcontacti s called eh
t pointof tangency or .
t c a t n o c f o t n i o p
Acommontangentis a ilne tangent to two circles( not necessarliy atthe )t n i o p e m a s
Circumference :theperimeter o fa circle ,thedistancearound a circle.d =
C π orC=2π r (d= diameter ,r=radius)
Areao fa circle=
A πr2
n o m m o c a s i R
M internal tangent
n o m m o c a s i S
N externaltangent
M
.
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.
P
N
R S
A
B
C
t n a c e S
t n e g n a T
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s n o g y l o P d e b i r c s m u c r i C d n a d e b i r c s n I
Inscribed :Apolygon i si nscribed f i ) n o g y l o p r e h t o n a r o ( e l c r i c a n ie l c r i c e h t n o e il s e c i t r e v s t i f o l l a
.) n o g y l o p r e h t o n a r o (
– The circlecenter i sthe
r e t n e c n
i o fthepolygon
Circumscribed :Apolygon i s at u o b a d e b i r c s m u c r i
c circle i f e h t o t t n e g n a t s i s e d i s s t i f o h c a e
. e l c r i c
– Thecircle centeri s the
r e t n e c m u c r i
c o fthepolygon
B
C
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. s n o i t s e u q e h t r e w s n a r o s d r o w t h g i r e h t h t i w k n a l b e h t l li F
.
1 _______________ consist o f2 endpointsand al lthe points i nbetween.
.
2 I feachangle i na trianglei sl essthan600 ,then thetriangle i scalled .
_ _ _ _ _ _ _ _ _ _ _ _
.
3 A ilnewhich meetsanother _____ at 900 iscalled a____________ ilne.
.
4 I ftwo angleso fa triangleareequa lto 450 ,then thetriangle i scalled _
_ _ _ _ _ _ _ _ _ _ _ _ _
.
5 I fwe ________ aright angle ,wewill havetwo________ angleso f450. .
6 I fthemeasure o fangleAi s 1300 ,then the _______________ i - 0s 23 0 .
.
7 Asegment thatperpendicular toa sideo ftrianglesand througha vertex .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ d e ll a c s i .
8 Eachtrianglehas 3points ,or _______________ .
9 ____________ i sarectanglewithf our congruent sides. .
0
1 An octagon i s________________ i na squarei fal lof i ts _____________ ileon .
e r a u q s e h t . 1
1 A____________withradius10 mhas____________________ o f20π m . .
2
1 Aquadr liatera lwhichonly hasonepair o fright angle can becalled .
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . 3
1 _______________________ hasseven verticesand _____ sides. .
4
1 I fthe________________________ o fasector i s 60 degrees ,thentheareao f _
_ _ _ _ _ _ _ _ _ _ _ _ _ s i r o t c e s e h
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. s n o i t s e u q e s e h t r e w s n A .
1 A right triangle has a hypotenuse o f6 and a perimeter o f14 .Find the . e l g n a i r t e h t f o a e r a .
2 Aregular hexagon is inscribed in a circle o fradius 4 meters .What is the ? n o g a x e h e h t f o a e r a .
3 The tota lnumber of i nterior anglesi n two regular polygons i s17 ,and the r a l u g e r h c a e s e o d s e d i s y n a m w o H . 3 5 s i s l a n o g a i d f o r e b m u n l a t o t ? e v a h n o g y l o p .
4 A triangle has sides o flength 30 ,40 ,and 50 meters .What is the length n a i r t s i h t f o e d u t i t l a t s e t r o h s e h t f
o gle?
.
5 A circle is inscribed in a triangle that has sides o flengths 60 ,80 ,and . e l c r i c e h t f o s u i d a r e h t f o h t g n e l e h t d n i F . m c 0 0 1 .
6 Five o fthe angles o fan octagon have measures whose sum is 8450 .O f
a e o t y r a t n e m e l p m o c e r a o w t , s e l g n a e e r h t g n i n i a m e r e h
t ch other and
e e r h t e s e h t f o s e r u s a e m e h t d n i F . r e h t o h c a e o t y r a t n e m e l p p u s e r a o w t . s e l g n a .
7 Gene wants to put a brick border around a tree .The border is to be , m c 2 5 . 6 5 s i e e r t e h t f o e c n e r e f m u c r i c e h t f I . e e r t e h t m o r f m 5 . 1 d e c a l p m u c r i c r e n n i e h t s i t a h
w ferenceo fthebrick border? .
8 A hexagon is inscribed in a circle ,which is inscribed in a square o fside ? n o g a x e h e h t f o e d i s h c a e f o h t g n e l e h t s i t a h W . m c 0 1 .
9 Find the dimension o f a rectangle o f maximum area with a given . P r e t e m i r e p . 0
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Describepoints ,ilnes ,and anglesi n these ifgurest
s
r
O
B
A
B
A
g
h
E
C
F
Q
O
B
f
A
g
h
