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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

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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
How can I make nanorobot?
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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