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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