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Inleiding

Die doel van hierdie hoofstuk is om van die meetkundige en trigonometriese beginsels, wat jy in die verlede teëgekom het, te hersien. Jy moet gemaklik wees met die werk wat behandel word in dié hoofstuk voor jy die Graad 10 Meetkunde Hoofstuk of die Graad 10 Trigonometrie Hoofstuk aanpak. Die hoofstuk hersien die volgende:

  1. Terminologie: vierhoeke, hoekpunte, sye, hoeke, parallele lyne, loodregte lyne, hoeklyne, halveerlyne en snylyne
  2. Ooreenstemmings en verskille tussen driehoeke en vierhoeke
  3. Eienskappe van driehoeke en vierhoeke
  4. Kongruensie
  5. Onderskeid tussen skerphoeke, regte hoeke, stomphoeke, reguitlyne en 'n volle omwenteling
  6. Pythagoras se Teorie, wat gebruik word om die sye van reghoekige driehoeke se lengtes te bereken

Punte en lyne

Die twee eenvoudigste elemente in meetkunde is punte en lyne .

ʼn Punt is ʼn koördinaat wat ʼn posisie in ruimte aandui (óf op ʼn getallelyn, óf in ʼn vlak óf in ʼn drie- of meerdimensionele ruimte) en word voorgestel deur ʼn dot. Punte word gewoonlik aangedui met ʼn hoofletter. ʼn Paar voorbeelde van hoe punte aangedui word, kan gesien word in [link] .

ʼn Lyn is ʼn stel kontinue koördinate in ʼn ruimte en kan gesien word as baie punte wat langs mekaar is. Lyne kan reguit of geboë wees, maar is altyd kontinu en dus is daar geen onderbrekings in lyne nie. Die eindpunte van lynstukke word met hoofletters aangedui. Voorbeelde van twee lyne word in [link] aangetoon.

Voorbeelde van ʼn paar punte (aangedui deur P , Q , R en S ) en ʼn paar lyne (aangedui deur B C en D E )

ʼn Lyn word aangedui deur ʼn beginpunt en ʼn eindpunt. Ons noem ʼn lyn wat begin by punt A en eindig by punt B , A B . Aangsien die lyn van punt B tot punt A dieselfde is as as die lyn van punt A tot die punt B , kan ons sê dat A B = B A .

Die lengte tussen die punte A en B is A B . Dus as ons sê A B = C D word dit bedoel dat die lengte van die lynstuk tussen A en B gelyk is aan die lengte tussen C en D .

ʼn Lyn word gemeet in eenhede van lengte . ʼn Paar voorbeelde van algemene eenhede van lengte word gelys in [link] .

’n Paar algemene eenhede van lengte en hul afkortings
Eenheid van lengte Afkorting
kilometer km
meter m
sentimeter cm
millimeter mm

Hoeke

ʼn Hoek word gevorm as twee lyne in ʼn gemeenskaplike punt ontmoet. Die punt waar twee lyne ontmoet staan bekend as die hoekpunt . Hoeke word aangedui deur ʼn ^ (kappie) bo 'n letter te plaas. Byvoorbeeld, in [link] is daar 'n hoek by B ^ . Hoeke kan ook aangedui word met behulp van die lyn segmente waaruit die hoek bestaan. Byvoorbeeld, in [link] word die hoek gevorm waar die lynsegmente C B en B A mekaar ontmoet. Die hoek kan dus aangedui word deur C B A of A B C . Die simbool dui 'n hoek in meetkunde aan.

Hoeke word gemeet in grade wat aangedui word deur die simbool (byvoorbeeld, 60 ).

Hoeke kan ook gemeet word in radiale. In die hoërskool sal ons slegs grade gebruik, maar in wiskunde op universiteitsvlak sal jy definitief weer radiale teëkom.

Hoek aangedui deur B ^ , C B A of A B C
Voorbeelde van hoeke. A ^ = E ^ , al is die lyne wat die verskillende hoeke vorm van verskillende lengtes

Meting van hoeke

Die grootte van ʼn hoek is onafhanklik van die lengtes van die twee sye wat die hoek onderspan. Dit hang slegs af van hoe die twee lyne relatief tot mekaar geplaas word, soos aangedui in [link] . ʼn Hoek vorm wanneer daar geroteer word om ʼn hoekpunt.

Questions & Answers

what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
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Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
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what is nano technology
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what is system testing?
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preparation of nanomaterial
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how to synthesize TiO2 nanoparticles by chemical methods
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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