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Wiskunde

Graad 9

Getalle

Module 3

Waarom is pythagoras so belangrik?

ONDERSOEK

1.1 Werk in ’n groep, maar begin eers alleen. Trek drie reghoekige driehoeke van verskillende vorms en groottes. Werk so akkuraat moontlik. As jy op blokkiespapier werk, is dit baie makliker. Werk nou nog meer akkuraat en meet die drie sye van elke driehoek. Werk tot die naaste millimeter. Vul die eerste drie rye van die tabel in. Gebruik nou ’n sakrekenaar om die tabel te voltooi.

SIMBOOL DRIEHOEK A DRIEHOEK B DRIEHOEK C
Lengte van die kortste sy a .................... .................... ....................
Lengte van middelste sy b .................... .................... ....................
Lengte van die langste sy c .................... .................... ....................
Kwadraat van lengte van kortste sy a 2 .................... .................... ....................
Kwadraat van lengte van middelste sy b 2 .................... .................... ....................
Som van die boonste twee kwadrate a 2 + b 2 .................... .................... ....................
Kwadraat van lengte van langste sy c 2 .................... .................... ....................

1.2 Daar behoort iets aan te gaan met die waardes in die gemerkte blokkies. In die groep, skryf neer presies wat julle waarneem en (as julle kan) wat die rede is.

  • ’n Mens kan die drie gegewe lyne gebruik om ’n reghoekige driehoek te vorm.

Uitknipwerk:

2.1 Kan ’n mens die drie gegewe vierhoeke ook gebruik om ’n driehoek te vorm?

3. Som die uitslag van hierdie ondersoek netjies op.

einde van ONDERSOEK

Die Stelling van Pythagoras lui:

  • In ’n reghoekige driehoek is die kwadraat van die skuinssy se lengte gelyk aan die som van die kwadrate van die lengtes van die ander twee sye.

Die belangrikheid van die Stelling van Pythagoras is dat ons dit op twee maniere gebruik: Eerstens, as ons weet dat ’n driehoek reghoekig is, dan kan ons iets belangriks sê oor die lengtes van die sye. Tweedens, as ons weet dat die drie sye van ’n driehoek die gegewe verband met mekaar het, dan moet die driehoek reghoekig wees.

KLASWERK

1. Ons benoem driehoeke soos volg:

  • Verwys na die skets hierlangs.
  • Die drie hoekpunte kry hoofletters as name. ( A , B en C )
  • Die sye kan benoem word as die twee hoekpuntewaartussen die sy lê ( AB , BC en AC ), of kleinletterskan gebruik word, dikwels dieselfde kleinletter as diehoekpunt oorkant die sy ( a , b en c ).
  • Ons werk hier met reghoekige driehoeke, maar hierdiebenoeming werk vir ander driehoeke ook.
  • Ons gebruik dieselfde letters vir beide die naam van ’n sy en vir die lengte van die sy.
  • Bv. PR = 3,5 cm of r = 5 cm.Δ PRS beteken: driehoek PRS

ONTHOU om altyd ’n liniaal te gebruik vir mooi sketse!

  • In die volgende oefeninge is die eerste probleem telkens ’n voorbeeld.

2. Probleem : Driehoek AEH het ’n regte hoek by H . AH = 6 cm en EH = 8 cm.Maak ’n skets (nie akkuraat nie) van die driehoek engebruik die Stelling van Pythagoras om die lengte vansy AE te bereken.

Oplossing : Omdat ons weet dat die driehoek ’nregte hoek het, mag ons sê dat AE 2 = AH 2 + EH 2 (of: h 2 = e 2 + a 2 )

Substitusie: AH 2 + EH 2 = (6) 2 + (8) 2 = 36 + 64 = 100 cm 2 As, dus, AE 2 = 100 cm 2 , dan is AE 10 cm.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
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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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