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Graad 8

Rasionale getalle, sirkels en driehoeke

Module 14

Om driehoeke te klassifiseer en te konstrueer



Om driehoeke te klassifiseer, belangrike stellings rondom driehoeke te ontdek en driehoeke te konstrueer

LU 3.1 LU 3.3 LU 3.4 LU 4.2.1
  • Jy sal aan die einde van hierdie leseenheid die volgende kan doen:
  • Verstaan hoe belangrik die gebruik van driehoeke in alledaagse situasies is;
  • Vir ander mense vertel hoe om ongekende sye van ‘n reghoekige driehoek uit te werk (Pythagoras);
  • Die oppervlakte van ‘n driehoek bereken;
  • Die aksie in meetkunde geniet;
  • Wiskundige taal gebruik om wiskundige idees, begrippe en veralgemenings en denkprosesse oor te dra.

1. Wanneer jy driehoeke klassifiseer, kan jy dit doen volgens hul hoeke, of volgens hul sye.

  • Klassifikasie op grond van die hoeke van ‘n driehoek:

Kan jy die volgende voltooi?

a) Skerphoekige driehoeke is driehoeke met

b) Reghoekige driehoeke het

c) Stomphoekige driehoeke het

  • Klassifikasie op grond van die sye van die driehoek:

Kan jy die volgende voltooi?

a) ‘n Gelybenige driehoek het

b) ‘n Gelyksydige driehoek het

c) ‘n Ongelyksydige driehoek se

2. Kan jy die volgende stellings voltooi rakende driehoeke? Maak ‘n skets om elk van die stellings prakties te illustreer.


  • Die som van die binnehoeke van enige driehoek is .........................
  • Skets:


  • Die buitehoek van ‘n driehoek is
  • Skets:

3. Konstruksie van driehoeke:

  • Benodigdhede: passer, gradeboog, potlood en ‘n liniaal


  • Maak altyd eers ‘n “rowwe sketsie” van hoe dit moontlik kan lyk.
  • Begin altyd met ‘n basislyn.

3.1 Konstrueer Δ size 12{Δ} {} PQR met PQ = 7 cm, PR = 5 cm en P ˆ size 12{ { hat {P}}} {} = 70°.

a) Skets:

b) Meet nou die volgende:

1. QR = ........ 2. R ˆ size 12{ { hat {R}}} {} = ........ 3. Q ˆ size 12{ { hat {Q}}} {} = ........ 4. P ˆ + Q ˆ + R ˆ = size 12{ { hat {P}}+ { hat {Q}}+ { hat {R}}={}} {} ........

3.2 Konstrueer Δ size 12{Δ} {} KLM , ‘n gelykbenige driehoek. KM = 40 mm, KL = LM en K ˆ size 12{ { hat {K}}} {} = 75°.Dui die groottes van al die hoeke op jou skets aan.

  • Skets:


Om die stelling van Pythagoras te ontdek en die berekening van die onbekende sye deur van die stelling gebruik te maak, te bemeester

LU 4.2.1 LU 4.8 LU 4.9 LU 4.10
  • Die volgende kan ‘n groepe gedoen word.

Prakties: Maak jou eie tangram

1. Sny ‘n vierkant (10 cm x 10 cm) uit karton.

2. Trek albei hoeklyne in, want dit moet deel vorm van die basisse van sommige figure.

3. Die volledige figuur moet uit die volgende bestaan:

3.1 twee groot gelykbenige driehoeke met basisse 10 cm elk

3.2 twee kleiner gelykbenige driehoeke met basisse 5 cm elk

3.3 een medium gelykbenige driehoek met twee aangrensende sye elk 5 cm

3.4 een vierkant met hoeklyne 5 cm

3.5 een parallelogram met twee oorstaande sye 5 cm

  • Jy moet twee hiervan maak.

4. Trek nou jou grootste driehoek van jou tangram in jou werkboek na.

5. Gebruik al sewe stukke en vorm ‘n vierkant daarmee en plaas dit op die skuinssy van jou nagetrekte driehoek.

6. Gebruik nou die twee grootste driehoeke en vorm ‘n vierkant daarmee en plaas dit op een van die reghoeksye van die nagetrekte driehoek.

7. Gebruik nou die oorblywende stukke en vorm ‘n vierkant daarmee en plaas dit op die ander reghoeksy.

8. Bereken die oppervlakte van elke vierkant .

Questions & Answers

what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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.
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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