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118 SSIMETRALA NA OTSE^KA. SIMETRALA NA AGOL19Potseti se! A
To~kata M e sredna to~ka na otse~-kata AB = 3 cm.
Odredi gi AM i MB.
Pravite a i b na crte`otse zaemno normalni.
Od koj vid e agolot !?
A M V
!
a b
1 Dadena e otse~kata AV. Niznejzinata sredna to~ka O po -vle~i prava s {to e normalnana otse~kata AV.
A V
s
O
Nacrtaj otse~ka AB.
Odredi ja srednata to~ka O naotse~kata AB.
!!
B
Niz to~kata O povle~i prava s normalna na AB.
Na kakvi delovi pravata s ja deli otse~kata AB?
Vo kakva zaemna polo`ba se pravata s i otse~kata AB?
M N
n sm
R
Pravata s {to ja prepolovuva otse~kata AB i e normal-na na nea vika simetrala na otse~kata AB.
Voo~i i zapomni!
Koja od pravite na crte`ot e simetrala na otse~kata MN?2
Nacrtaj otse~ka CD i potoa nacrtaj ja nejzinata simetrala s.3
Na crte`ot e daden ! AOB = 68o i vo negovata oblast epovle~ena poluprava OC taka {to ! AOC = 34o.
Razgledaj go crte`ot i odgovori na pra{aweto.
Kolku stepeni ima ! COB?
Na kakvi delovi polupravata OC go deli agolot AOB?
4
O A
C
B
Zaklu~iv! Polupravata OC godeli agolot AOB na dva ednakvidela. ! AOB = 68o, ! AOC = 34o i ! COB = 34o.
Polupravata {to go deli eden agol nadva ednakvi agli se vika simetralana toj agol.
Zapomni!
!!!
118 SSIMETRALA NA OTSE^KA. SIMETRALA NA AGOL19Potseti se! A
To~kata M e sredna to~ka na otse~-kata AB = 3 cm.
Odredi gi AM i MB.
Pravite a i b na crte`otse zaemno normalni.
Od koj vid e agolot !?
A M V
!
a b
1 Dadena e otse~kata AV. Niznejzinata sredna to~ka O po -vle~i prava s {to e normalnana otse~kata AV.
A V
s
O
Nacrtaj otse~ka AB.
Odredi ja srednata to~ka O naotse~kata AB.
!!
B
Niz to~kata O povle~i prava s normalna na AB.
Na kakvi delovi pravata s ja deli otse~kata AB?
Vo kakva zaemna polo`ba se pravata s i otse~kata AB?
M N
n sm
R
Pravata s {to ja prepolovuva otse~kata AB i e normal-na na nea vika simetrala na otse~kata AB.
Voo~i i zapomni!
Koja od pravite na crte`ot e simetrala na otse~kata MN?2
Nacrtaj otse~ka CD i potoa nacrtaj ja nejzinata simetrala s.3
Na crte`ot e daden ! AOB = 68o i vo negovata oblast epovle~ena poluprava OC taka {to ! AOC = 34o.
Razgledaj go crte`ot i odgovori na pra{aweto.
Kolku stepeni ima ! COB?
Na kakvi delovi polupravata OC go deli agolot AOB?
4
O A
C
B
Zaklu~iv! Polupravata OC godeli agolot AOB na dva ednakvidela. ! AOB = 68o, ! AOC = 34o i ! COB = 34o.
Polupravata {to go deli eden agol nadva ednakvi agli se vika simetralana toj agol.
Zapomni!
!!!
118 SSIMETRALA NA OTSE^KA. SIMETRALA NA AGOL19Potseti se! A
To~kata M e sredna to~ka na otse~-kata AB = 3 cm.
Odredi gi AM i MB.
Pravite a i b na crte`otse zaemno normalni.
Od koj vid e agolot !?
A M V
!
a b
1 Dadena e otse~kata AV. Niznejzinata sredna to~ka O po -vle~i prava s {to e normalnana otse~kata AV.
A V
s
O
Nacrtaj otse~ka AB.
Odredi ja srednata to~ka O naotse~kata AB.
!!
B
Niz to~kata O povle~i prava s normalna na AB.
Na kakvi delovi pravata s ja deli otse~kata AB?
Vo kakva zaemna polo`ba se pravata s i otse~kata AB?
M N
n sm
R
Pravata s {to ja prepolovuva otse~kata AB i e normal-na na nea vika simetrala na otse~kata AB.
Voo~i i zapomni!
Koja od pravite na crte`ot e simetrala na otse~kata MN?2
Nacrtaj otse~ka CD i potoa nacrtaj ja nejzinata simetrala s.3
Na crte`ot e daden ! AOB = 68o i vo negovata oblast epovle~ena poluprava OC taka {to ! AOC = 34o.
Razgledaj go crte`ot i odgovori na pra{aweto.
Kolku stepeni ima ! COB?
Na kakvi delovi polupravata OC go deli agolot AOB?
4
O A
C
B
Zaklu~iv! Polupravata OC godeli agolot AOB na dva ednakvidela. ! AOB = 68o, ! AOC = 34o i ! COB = 34o.
Polupravata {to go deli eden agol nadva ednakvi agli se vika simetralana toj agol.
Zapomni!
!!!
118 SSIMETRALA NA OTSE^KA. SIMETRALA NA AGOL19Potseti se! A
To~kata M e sredna to~ka na otse~-kata AB = 3 cm.
Odredi gi AM i MB.
Pravite a i b na crte`otse zaemno normalni.
Od koj vid e agolot !?
A M V
!
a b
1 Dadena e otse~kata AV. Niznejzinata sredna to~ka O po -vle~i prava s {to e normalnana otse~kata AV.
A V
s
O
Nacrtaj otse~ka AB.
Odredi ja srednata to~ka O naotse~kata AB.
!!
B
Niz to~kata O povle~i prava s normalna na AB.
Na kakvi delovi pravata s ja deli otse~kata AB?
Vo kakva zaemna polo`ba se pravata s i otse~kata AB?
M N
n sm
R
Pravata s {to ja prepolovuva otse~kata AB i e normal-na na nea vika simetrala na otse~kata AB.
Voo~i i zapomni!
Koja od pravite na crte`ot e simetrala na otse~kata MN?2
Nacrtaj otse~ka CD i potoa nacrtaj ja nejzinata simetrala s.3
Na crte`ot e daden ! AOB = 68o i vo negovata oblast epovle~ena poluprava OC taka {to ! AOC = 34o.
Razgledaj go crte`ot i odgovori na pra{aweto.
Kolku stepeni ima ! COB?
Na kakvi delovi polupravata OC go deli agolot AOB?
4
O A
C
B
Zaklu~iv! Polupravata OC godeli agolot AOB na dva ednakvidela. ! AOB = 68o, ! AOC = 34o i ! COB = 34o.
Polupravata {to go deli eden agol nadva ednakvi agli se vika simetralana toj agol.
Zapomni!
!!!
184 MMERKI ZA DOL@INA, MASA I TE^NOST1Potseti se! ANa linijarot poka`i dol -`i ni od 1 dm, 3 cm, 8 mm i4 cm 6 mm.
Koja merka se koristi zamerewe dol`ina napati{tata i rasto janieme|u dve naseleni mesta?
Kolku dekagrami ima vo 1 kg?
Koja merka se koristi zamerewe masa na rudaiskopana od rudnik?
Kolku dl ima vo 1 l?
MERKI ZA DOL@INA
1 Proceni gi dol`inite na otse~kite AB i CD ina iskr{enata linija PQRST, a potoa, somerewe proveri ja to~nosta na tvojata procenka.
A
C
VD
P R T
Q S
Koi merni edinici gi upotrebi?
Nabroj i drugi merki za dol`ina {to gi znae{.
Pogolemi i pomali merni edinici od metarot se prika`ani vo slednata tabela.
Osnovna merna edinica za dol`ina e metar (m).
Pogolemi merni edi -nici od metarot se:dekametar (dam)hektometar (hm)kilometar (km)
Pomali merni edi-nici od metarot se:decimetar (dm)centimetar (cm)
milimetar (mm)
1 dam1 m1 hm
1 km
1 dm1 cm1 mm
Voo~i gi i zapomni gi vrskite me|u merkite za dol`ina!
1 km = 10 hm = 100 dam = 1000 m1 hm = 10 dam = 100 m
1 dam = 10 m1 m = 10 dm = 100 cm = 1000 mm
1 dm = 10 cm = 100 mm1 cm = 10 mm
Da zapomnam! Sekoja mernaedinica za dol`ina e 10 pa -ti pomala od mernataedinica {to e neposrednopogolema od nea.
Koja merka bi trebalo da stoi na mestoto na “!”.
Za 1 ~as, Petar mo`e da izodi okolu 4 !.
2
Mimoza vo tetratkata nacrtala kvadrat so dol`ina na stranata 30 !.
Kolku dekametri ima vo a) 90 m? b) 300 m? v) 1700 m?
3 Vo 1 dm ima 0,1 m. Kolku metri ima vo 1 cm?4
!
" 1000
" 100
" 10
: 1000
: 100
: 10
204 Da zapomnam! Edna mer ka za volumen e 1 000 pati pogolema odnepo sredno poma lata merka.
Vo pregledot e daden odnosot me|u mernite edinici za volumen.
1 m3 = 1 000 dm3 1 dm3 = 1 000 cm3
= 1 000 000 cm3 = 1 000 000 mm3
= 1 000 000 000 mm3 1 cm3 = 1 000 mm3
2 Objasni zo{to 1 dm3 ima 1 000 cm3.
Voo~i go crte`ot i raboti spored postapkata.
Kolku kocki so volumen 1 cm3 mo`e{ da naredi{ edna do druga po rabot na kocka so volumen 1 dm3?
Kolku takvi redovi ti se potrebni za da ja pokrie{ osnovata na kockata od 1 dm3?
Kolku takvi sloevi ti se potrebni za da ja ispolni{ kockata od 1 dm3?
10
9
8
7
6
5
4
3
2
1 2 3 4 5 6 7 8 9 10
109
87
65
43
21
145
1. 3.
1 m2.
1 m2 = 100 dm2; 1 m2 = 10 000 cm2.
2 = cm2 2 = cm2;2 = cm2 2 = cm2.
5.
2 = dm2 2 = dm2;2 = dm2 2 = dm2.
4.
2
7 dm2 = cm2; 4 m2 = cm2.
2.
2
2 = cm2;2 18 cm2 = cm2;
2 = dm2;2 25 dm2 = dm2.
2
2
1 m2
48 dm2
2.
4.
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Matematika memo Mjerne jedinice
Artmedia Varaždin 2008 • www.artrea.com.hr
Jedinica za duljinu - metar1 km = 1000 m1 m = 10 dm = 100 cm = 1000 mm1 dm = 10 cm = 100 cm1 cm = 10 mm1 mm
Jedinica za masu - kilogram1 t = 1000 kg1 kg = 100 dag = 1000 g1 dag = 10 g1 g = 1000 mg
Jedinica za površinu - metar kvadratni2 21 km = 100 ha = 10 000 a =1 000 000 m21 ha = 100 a = 10 000 m21 a = 100 m2 2 2 21 m = 100 dm = 10 000 cm = 1 000 000 mm2 2 21 dm = 100 cm = 10 000 mm2 21 cm = 100 mm
Jedinica za vrijeme - sat1 d = 24 h = 1440 min1 h = 60 min = 360 s1 min = 60 s1 s = 1000 ms
1 nautièka milja = 1852 m 1 yard = 0,914 m 1 funta = 453,6 g1 inch = 2,54 cm 1 gallon = 3,785 l 1 karat = 0,2053 g
tonakilogramdekagramgramdansatminutasekunda
kvadratni kilometarhektararkvadratni metarkvadratni decimetarkvadratni centimetar
Jedinica za obujam - metar kubni3 31 km = 1 000 000 000 m
3 3 31 m = 1000 dm = 1 000 000 cm3 3 3 1 dm = 1000 cm = 1 000 000 mm = 1 litar3 31 cm = 1000 m
kilometarmetardecimetarcentimetarmilimetarkubni kilometarkubni metarkubni decimetarkubni centimetarMatematika memo Mjerne jedinice
Artmedia Varaždin 2008 • www.artrea.com.hr
Jedinica za duljinu - metar1 km = 1000 m1 m = 10 dm = 100 cm = 1000 mm1 dm = 10 cm = 100 cm1 cm = 10 mm1 mm
Jedinica za masu - kilogram1 t = 1000 kg1 kg = 100 dag = 1000 g1 dag = 10 g1 g = 1000 mg
Jedinica za površinu - metar kvadratni2 21 km = 100 ha = 10 000 a =1 000 000 m21 ha = 100 a = 10 000 m21 a = 100 m2 2 2 21 m = 100 dm = 10 000 cm = 1 000 000 mm2 2 21 dm = 100 cm = 10 000 mm2 21 cm = 100 mm
Jedinica za vrijeme - sat1 d = 24 h = 1440 min1 h = 60 min = 360 s1 min = 60 s1 s = 1000 ms
1 nautièka milja = 1852 m 1 yard = 0,914 m 1 funta = 453,6 g1 inch = 2,54 cm 1 gallon = 3,785 l 1 karat = 0,2053 g
tonakilogramdekagramgramdansatminutasekunda
kvadratni kilometarhektararkvadratni metarkvadratni decimetarkvadratni centimetar
Jedinica za obujam - metar kubni3 31 km = 1 000 000 000 m
3 3 31 m = 1000 dm = 1 000 000 cm3 3 3 1 dm = 1000 cm = 1 000 000 mm = 1 litar3 31 cm = 1000 m
kilometarmetardecimetarcentimetarmilimetarkubni kilometarkubni metarkubni decimetarkubni centimetarMatematika memo Mjerne jedinice
Artmedia Varaždin 2008 • www.artrea.com.hr
Jedinica za duljinu - metar1 km = 1000 m1 m = 10 dm = 100 cm = 1000 mm1 dm = 10 cm = 100 cm1 cm = 10 mm1 mm
Jedinica za masu - kilogram1 t = 1000 kg1 kg = 100 dag = 1000 g1 dag = 10 g1 g = 1000 mg
Jedinica za površinu - metar kvadratni2 21 km = 100 ha = 10 000 a =1 000 000 m21 ha = 100 a = 10 000 m21 a = 100 m2 2 2 21 m = 100 dm = 10 000 cm = 1 000 000 mm2 2 21 dm = 100 cm = 10 000 mm2 21 cm = 100 mm
Jedinica za vrijeme - sat1 d = 24 h = 1440 min1 h = 60 min = 360 s1 min = 60 s1 s = 1000 ms
1 nautièka milja = 1852 m 1 yard = 0,914 m 1 funta = 453,6 g1 inch = 2,54 cm 1 gallon = 3,785 l 1 karat = 0,2053 g
tonakilogramdekagramgramdansatminutasekunda
kvadratni kilometarhektararkvadratni metarkvadratni decimetarkvadratni centimetar
Jedinica za obujam - metar kubni3 31 km = 1 000 000 000 m
3 3 31 m = 1000 dm = 1 000 000 cm3 3 3 1 dm = 1000 cm = 1 000 000 mm = 1 litar3 31 cm = 1000 m
kilometarmetardecimetarcentimetarmilimetarkubni kilometarkubni metarkubni decimetarkubni centimetar