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Graad 9

Algebra en meetkunde

Module 10



Om prakties die voorwaardes van gelykvormigheid te ondersoek

1. Die vyfhoeke ABDEF en LCMRK word gegee (A-6). LCMRK is ‘n vergroting van ABDEF. Wat is die skaalfaktor waarmee ABDEF vergroot is om LCMRK te gee?

2. Skryf die verhoudings tussen die ooreenstemmende pare sye van ABDEF en LCMRK neer.

3. Skryf die verwantskap tussen die ooreenstemmende pare hoeke van die twee figure neer.

4. Hierdie twee figure is nie kongruent nie. Wat noem ons hulle?

5. Noem soveel moontlik voorbeelde in die alledaagse lewe van hierdie verskynsel.

Gelykvormige figure.

Die vyfhoeke in die aktiwiteit hierbo is gelykvormig. Hulle het dieselfde vorm, maar is nie ewe groot nie.

Hulle ooreenstemmende hoeke het dieselfde grootte.

Hulle ooreenstemmende sye is in dieselfde verhouding.

Dus is LK AF = KR FE = MR DE = CM BD = CL BA = 3 1 size 12{ { { ital "LK"} over { ital "AF"} } = { { ital "KR"} over { ital "FE"} } = { { ital "MR"} over { ital "DE"} } = { { ital "CM"} over { ital "BD"} } = { { ital "CL"} over { ital "BA"} } = { {3} over {1} } } {} Hierdie konstante verhouding is ook die skaalfaktor van die vergroting.

Ons sê dat ABDEF  LCMRK. Let daarop dat die volgorde van die letters in dieselfde volgorde van die hoeke wat gelyk is en die sye wat in verhouding is, geskryf word. (Die simbool vir gelykvormigheid is ).


1. Meet die lengtes van die sye en die groottes van die hoeke in die volgende figure (A-7) en besluit of hulle gelykvormig is of nie. As die twee figure nie gelykvormig is nie, gee die rede hoekom hulle nie gelykvormig is nie.

2. As twee vierhoeke se ooreenstemmende hoeke gelyk is, is hulle noodwendig ook gelykvormig ?

3. As twee vierhoeke se sye in dieselfde verhouding is, is hulle noodwendig ook gelykvormig ?

In bostaande huiswerkopdrag het jy gesien dat, vir vierhoeke om gelykvormig te wees, aan albei voorwaardes van gelykvormigheid voldoen moet word, met ander woorde, die ooreenstemmende hoeke moet gelyk wees en die ooreenstemmende sye moet in dieselfde verhouding wees. Geld dieselfde ook vir driehoeke?


Om prakties die voorwaardes van gelykvormigheid by driehoeke te ondersoek

[LU 3.5]


Konstrueer ΔABC en ΔDEF. Bereken die grootte van A en E.

1.2 Is die ooreenstemmende hoeke van die twee driehoeke gelyk?

1.3 Voltooi die volgende:

AB ED = size 12{ { { ital "AB"} over { ital "ED"} } ={}} {} ....................

BC DF = size 12{ { { ital "BC"} over { ital "DF"} } ={}} {} ....................

AC EF = size 12{ { { ital "AC"} over { ital "EF"} } ={}} {} ....................

1.4 Is die ooreenstemmende sye van die twee driehoeke in dieselfde verhouding?

1.5 Is die twee driehoeke gelykvormig?

1.6 Voltooi die volgende: As twee driehoeke se ooreenstemmende hoeke gelyk is, is hulle ooreenstemmende sye noodwendig altyd ......................... Dit beteken dus dat, as driehoeke se ooreenstemmende hoeke gelyk is, is die driehoeke .........................

2.1 Konstrueer die volgende twee driehoeke:

2.2 Is die sye van die twee driehoeke in dieselfde verhouding?

2.3 Meet al die hoeke van ΔABC en ΔMOR. Wat vind jy?

2.4 Is die ΔABC  ΔMOR?

2.5 Voltooi die volgende: As twee driehoeke se ooreenstemmende sye in dieselfde verhouding is, is hulle ooreenstemmende ..................................... gelyk. Dit beteken dus dat, as driehoeke se ooreenstemmende sye in dieselfde verhouding is, is die driehoeke .....................................

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
Got questions? Join the online conversation and get instant answers!
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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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