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Wiskunde

Graad 9

Algebra en meetkunde

Module 9

Kongruensie

  • Kongruensie beteken dat twee figure in alle opsigte identies is. Dit beteken dus dat al die sye van die een figuur gelyk is aan al die sye van die ander figuur. Dit beteken ook dat al die hoeke van die een figuur gelyk is aan al die hoeke van die ander figuur. As die figure uitgeknip word, sal al die kongruente figure dus presies op mekaar pas.

AKTIWITEIT 1

Om te verstaan wat die begrip kongruensie in die algemeen beteken

[LU 3.2.1]

Kyk na die figure op die bladsy met blokkies (A-1) en besluit watter figure kongruent is. Gee dan elke paar kongruente figure deur die letters in die volgorde van sye en hoeke wat gelyk is, te gee. Die simbool vir kongruensie is 

Byvoorbeeld:

Vierhoek APEK  Vierhoek CDNM

  • ‘n Driehoek het ses elemente; naamlik drie hoeke en drie sye. Net drie van hierdie elemente is nodig om ‘n driehoek te konstrueer:
  • Kombinasies van die drie elemente is:
  • 3 sye (sss)
  • 2 sye en die hoek tussen hulle (ss)
  • 2 hoeke en ‘n sy (s)
  • 2 sye en die hoek nie tussen hulle nie (ss)
  • 3 hoeke ()
  • ‘n 90° - hoek, ‘n reghoeksy en die skuinssy (90°ss)

AKTIWITEIT 2

Om prakties uit te vind wat die voorwaardes van kongruensie van driehoeke is.

  • Jy word vier bladsye met akkuraat gekonstrueerde driehoeke gegee.

1.1 Bestudeer bladsy A-2 van die akkuraat gekonstrueerde driehoeke. Kyk na al die driehoeke wat gekonstrueer is deurdat drie sye gebruik is en gee al die pare driehoeke wat kongruent is. (sss) . Onthou dat, soos in aktiwiteit 1, die driehoeke gegee moet word in die volgorde van die sye wat gelyk is aan mekaar.

1.2 Sal twee driehoeke waarvan die sye van die een driehoek gelyk is aan die sye van die ander driehoek altyd kongruent wees aan mekaar?

1.3 As jy slegs die inligting, soos in die sketse hieronder, kry, sal jy met sekerheid kan sê dat die twee driehoeke altyd kongruent is? (Onthou geen werklike lengtes word gegee nie).

2.1 Bestudeer weer bladsy A-2 van die akkuraat gekonstrueerde driehoeke. Kyk nou na al die driehoeke wat gekonstrueer is deurdat twee sye en ‘n ingeslote hoek gebruik is om hulle te konstrueer, (s s) , en gee al die pare driehoeke wat kongruent is. Onthou weer dat die driehoeke gegee moet word in volgorde van die sy, hoek en sy wat gelyk is.

2.2 Sal twee driehoeke waarvan die twee sye en die hoek tussen die twee gegewe sye, gelyk is, altyd kongruent wees?

2.3 As jy slegs die inligting, soos in die sketse hieronder, kry, sal jy met sekerheid kan sê dat die twee driehoeke altyd kongruent is? (Geen werklike sylengtes en hoekgroottes word gegee nie).

3.1 Op bladsy A-3 van die akkuraat gekonstrueerde driehoeke word twee hoeke en ‘n sy gebruik (  s) om die driehoeke te konstrueer. Bestudeer hierdie driehoeke en skryf die pare driehoeke neer wat kongruent is. Onthou weer om die driehoeke te skryf in volgorde van die elemente wat gelyk is.

3.2 In ΔDOM en ΔLOC is DM = OC, D = O en M = L, maar tóg is die twee driehoeke nie kongruent nie. Hoekom is dit so? Gee ‘n algemene reël deur die volgende sin te voltooi:

Twee driehoeke is kongruent as hoek, hoek, sy = hoek, hoek, en die ...................... sy.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
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
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
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
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
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Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
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Yasmin
what is the function of carbon nanotubes?
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I'm interested in nanotube
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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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