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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

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
Do somebody tell me a best nano engineering book for beginners?
s. Reply
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?
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
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what is biological synthesis of nanoparticles
Sanket 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
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what is the function of carbon nanotubes?
I'm interested in nanotube
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
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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