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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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