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Wiskunde

Graad 9

Vierkante, perspektieftekening, transformasies

Module 22

Vergelyking van vierhoeke ten opsigte van verskille en ooreenkomste

AKTIWITEIT 1

Om vierhoeke te vergelyk ten opsigte van ooreenkomste en verskille

[LU 3.4]

1. Vergelykings

Werk saam in klein groepies aan die volgende oefening. Vergelyk die pare vierhoeke wat hieronder aangegee word. Skryf neer in watter opsigte hulle eenders is en hoe hulle verskil. Probeer om te sê hoe om die een in die ander te verander – as jy dit kan doen, dan verstaan jy hul eienskappe werklik. As ‘n voorbeeld, kyk na die vraag aan die einde van deel 3 hierbo oor ewewydige sye.

Elke groep moet met ten minste een paar vierhoeke werk. As jy met ‘n vlieër werk, ondersoek beide soorte vlieërs.

  • Ruit en vierkant
  • Trapesium en parallelogram
  • Vierkant en reghoek
  • Vlieër en ruit
  • Parallelogram en vlieër
  • Reghoek en trapesium

As jy hierby nóg ‘n paar vierhoeke wil vergelyk, doen dit gerus!

1. Definisies

‘n Kort en akkurate beskrywing van ‘n vierhoek volgens hierdie eienskappe word ‘n definisie genoem. ‘n Definisie is ondubbelsinnig, sodat dit slegs op een vierhoek van toepassing is, en sodat ons dit kan gebruik om tussen soorte vierhoeke te onderskei.

Die definisies word in ‘n sekere orde aangegee, want die latere definisies verwys na vorige definisies om hulle korter en makliker verstaanbaar te maak. Daar bestaan meer as een stel definisies; hier volg een so ‘n stel.

  • ‘n Vierhoek is ‘n vlak figuur begrens deur vier reguit lyne.
  • ‘n Vlieër is ’n vierhoek met twee paar aanliggende gelyke sye.
  • ‘n Trapesium is ‘n vierhoek met een paar ewewydige teenoorstaande sye.
  • ‘n Parallelogram is ‘n vierhoek met twee paar ewewydige teenoorstaande sye.
  • ‘n Ruit is ‘n parallelogram met gelyke aanliggende sye.
  • ‘n Vierkant is ‘n ruit met vier gelyke binnehoeke.
  • ‘n Reghoek is ‘n parallelogram met vier gelyke binnehoeke.

AKTIWITEIT 2

Om informeel formules vir die oppervlaktes van vierhoeke te ontwikkel

[LU 3.4]

Bereken oppervlaktes van plat figure

  • Ons begin by die oppervlaktes van driehoeke: Julle het dalk al die woorde, “half basis maal hoogte” gehoor. Dis die formule vir die oppervlakte van ‘n driehoek. Ons gebruik A vir die oppervlakte , h vir die hoogte en b vir die basis .
  • Oppervlakte = ½ × basis × hoogte; A = ½ bh ; A = bh 2 size 12{ { { ital "bh"} over {2} } } {} is verskeie weergawes van die formule.
  • Wat is nou eintlik die basis ? En wat is die hoogte ? Wat belangrik is, is dat die hoogte en die basis saam hoort: die basis is nie net sommer enige sy nie, en die hoogte nie sommer net enige lyn nie.
  • Die hoogte is altyd ‘n lyn wat loodreg is op dié sy wat jy die basis noem. Verwys na die sketse hierbo. Die basis en sy ooreenstemmende hoogte is donker lyne. Hieronder is nog drie voorbeelde van basis/hoogte-pare.
  • Trek met twee ander kleure die ander twee basis/hoogte-pare in elk van die boonste ses driehoeke, elke paar in sy eie kleur. Doen daarna die volgende oefening:

Kies een van die driehoeke en bereken sy oppervlakte drie keer. Meet die lengtes met jou liniaal en gebruik elke slag ‘n ander basis/hoogte-paar vir jou berekening. Stem die antwoorde grootliks ooreen? Indien nie, meet weer versigtig en doen weer die som.

Questions & Answers

what is the stm
Brian Reply
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 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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
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
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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