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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


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.

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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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