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Grade 8

Verhoudings en eweredigheid

Meting en vormleer


Module 17

Konstruksie van verskillende soorte hoeke


Om verskillende soorte hoeke en driehoeke te konstrueer

[LU 3.4, 3.5, 4.7]

1. Hoe om ‘n hoek te teken:Benodigdhede: potlood, liniaal, gradeboog.

1.1 Begin altyd met ‘n basislyn.

1.2 Maak ‘n merkie vir ‘n begin bv. links en plaas jou gradeboog op jou merkie.

1.3 Lees óf van die buitekant óf die binnekant van jou gradeboog vanaf 0°.

1.4 By hoeke groter as 180° moet jy eers die bepaalde hoek van 360° aftrek, en dan daardie betrokke hoek teken. Die hoek buitekant om (die inspringende hoek) sal dan die betrokke hoek wees wat jy moet teken.Bv. 320°: (360° – 320° = 40°). Teken nou ‘n hoek van 40°. Die inspringende hoek verteenwoordig nou die 320°.

2. Konstrueer nou die volgende hoeke en benoem elke hoek:

  • A B ˆ size 12{ { hat {B}}} {} C = 75°

Soort hoek: ______

2.2 C D ˆ size 12{ { hat {D}}} {} E = 135°

Soort hoek: ______

2.3 F G ˆ size 12{ { hat {G}}} {} H = 215°

Soort hoek: ______

3. Hoe om ‘n driehoek te konstrueer:

Benodigdhede: potlood, liniaal, gradeboog en passer.

  • Begin altyd eers deur ‘n rowwe skets te maak.
  • Gebruik dan een van die sye waarvan die lengte gegee is, as basis.
  • Bv. konstrueer Δ size 12{Δ} {} ABC met BC = 40 mm, B ˆ size 12{ { hat {B}}} {} = 70° en C ˆ size 12{ { hat {C}}} {} = 50°.

Rowwe skets:

  • Om ‘n sylengte akkuraat te meet moet jy die lengte met jou passer op jou liniaal meet en dan jou passer se punt op B sit en met die potlood ‘n “kapmerk” maak waar C moet wees.
  • Konstruksie:

4. Konstrueer nou elk van die volgende driehoeke:

4.2 Δ size 12{Δ} {} PQR met QR = 58 mm, P Q ˆ size 12{ { hat {Q}}} {} R = 62° en Q P ˆ size 12{ { hat {P}}} {} R = 69°.


  1. PQ = mm
  2. R ˆ size 12{ { hat {R}}} {} =

4.2 Gelykbenige Δ size 12{Δ} {} ABC met BC = 42 mm, AB = AC en B ˆ size 12{ { hat {B}}} {} = 63°.


a) PQ = mm


Om enige gegewe lyn of hoek te halveer [LU 3.4, 3.5, 4.7]

  1. Halvering van ‘n gegewe lyn AB :
  • Meet lynstuk AB (bv. 40 mm).
  • Neem jou passer en meet bietjie meer as die helfte van jou lyn (d.w.s. ± 22-25 mm).
  • Plaas jou passer se skerppunt op A en maak ‘n “kapmerk” onder en bo die lyn.
  • Plaas dan jou passer op B en maak ook ‘n “kapmerk” bo en onder die lyn.
  • Verbind die kruispunte van die twee “kapmerke” met mekaar.
  • Benoem die punt op lyn AB , P. P is nou die middelpunt van lyn AB .

2. Probeer nou self die volgende:

  • Teken ‘n lynstuk PQ = 70 mm.
  • Halveer nou lynstuk PQ , soos in nr. 1 verduidelik.

3. Halvering van π ABC :

  • Plaas jou passer se skerppunt op B .
  • Trek enige grootte boog soos aangedui.
  • Plaas jou passer se punt op die punt waar die twee lyne mekaar kruis en maak ‘n “kapmerk” binne die hoek.
  • Plaas nou jou passer se punt op die ander punt waar die twee lyne mekaar kruis en maak ‘n “kapmerk” binne die hoek, sodat jou twee “kapmerke” mekaar kruis.
  • Verbind B ˆ size 12{ { hat {B}}} {} (hoek B ) met die plek waar jou “kapmerke” mekaar kruis.
  • B ˆ size 12{ { hat {B}}} {} 1 sal nou net so groot wees soos B ˆ size 12{ { hat {B}}} {} 2 . Meet beide hoeke. Is hulle ewe groot?

4. Probeer nou self die volgende doen:

  • Teken D E ˆ size 12{ { hat {E}}} {} F . = 125°.
  • Halveer nou D E ˆ size 12{ { hat {E}}} {} F .


Om ‘n loodlyn vanuit ‘n punt op ‘n lyn te konstrueer [LU 3.4, 3.5, 4.7]

1. Konstrueer AD size 12{ ortho } {} BC .

  • Plaas jou passer se skerppunt op A (want jy wil uit A ‘n lyn loodreg op BC trek.)
  • Maak nou ‘n boog op BC .
  • Plaas jou passer se punt eers op die een punt waar die boog en BC mekaar kruis en maak ‘n “kapmerk” onder BC en dan op die ander kruispunt en maak weer ‘n “kapmerk” onder BC , sodat jou twee “kapmerke” mekaar kruis.
  • Verbind nou A met die kruispunt van die twee “kapmerke”.
  • Merk die plek waar die twee lyne mekaar sny, D .
  • AD is nou loodreg op BC . ( AD size 12{ ortho } {} BC .)

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
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
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
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
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.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Wiskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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