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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

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
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 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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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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