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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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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