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Wiskunde

Graad 9

Vierkante, perspektieftekening, transformasies

Module 22

Vergelyking van vierhoeke ten opsigte van verskille en ooreenkomste

AKTIWITEIT 1

Om vierhoeke te vergelyk ten opsigte van ooreenkomste en verskille

[LU 3.4]

1. Vergelykings

Werk saam in klein groepies aan die volgende oefening. Vergelyk die pare vierhoeke wat hieronder aangegee word. Skryf neer in watter opsigte hulle eenders is en hoe hulle verskil. Probeer om te sê hoe om die een in die ander te verander – as jy dit kan doen, dan verstaan jy hul eienskappe werklik. As ‘n voorbeeld, kyk na die vraag aan die einde van deel 3 hierbo oor ewewydige sye.

Elke groep moet met ten minste een paar vierhoeke werk. As jy met ‘n vlieër werk, ondersoek beide soorte vlieërs.

  • Ruit en vierkant
  • Trapesium en parallelogram
  • Vierkant en reghoek
  • Vlieër en ruit
  • Parallelogram en vlieër
  • Reghoek en trapesium

As jy hierby nóg ‘n paar vierhoeke wil vergelyk, doen dit gerus!

1. Definisies

‘n Kort en akkurate beskrywing van ‘n vierhoek volgens hierdie eienskappe word ‘n definisie genoem. ‘n Definisie is ondubbelsinnig, sodat dit slegs op een vierhoek van toepassing is, en sodat ons dit kan gebruik om tussen soorte vierhoeke te onderskei.

Die definisies word in ‘n sekere orde aangegee, want die latere definisies verwys na vorige definisies om hulle korter en makliker verstaanbaar te maak. Daar bestaan meer as een stel definisies; hier volg een so ‘n stel.

  • ‘n Vierhoek is ‘n vlak figuur begrens deur vier reguit lyne.
  • ‘n Vlieër is ’n vierhoek met twee paar aanliggende gelyke sye.
  • ‘n Trapesium is ‘n vierhoek met een paar ewewydige teenoorstaande sye.
  • ‘n Parallelogram is ‘n vierhoek met twee paar ewewydige teenoorstaande sye.
  • ‘n Ruit is ‘n parallelogram met gelyke aanliggende sye.
  • ‘n Vierkant is ‘n ruit met vier gelyke binnehoeke.
  • ‘n Reghoek is ‘n parallelogram met vier gelyke binnehoeke.

AKTIWITEIT 2

Om informeel formules vir die oppervlaktes van vierhoeke te ontwikkel

[LU 3.4]

Bereken oppervlaktes van plat figure

  • Ons begin by die oppervlaktes van driehoeke: Julle het dalk al die woorde, “half basis maal hoogte” gehoor. Dis die formule vir die oppervlakte van ‘n driehoek. Ons gebruik A vir die oppervlakte , h vir die hoogte en b vir die basis .
  • Oppervlakte = ½ × basis × hoogte; A = ½ bh ; A = bh 2 size 12{ { { ital "bh"} over {2} } } {} is verskeie weergawes van die formule.
  • Wat is nou eintlik die basis ? En wat is die hoogte ? Wat belangrik is, is dat die hoogte en die basis saam hoort: die basis is nie net sommer enige sy nie, en die hoogte nie sommer net enige lyn nie.
  • Die hoogte is altyd ‘n lyn wat loodreg is op dié sy wat jy die basis noem. Verwys na die sketse hierbo. Die basis en sy ooreenstemmende hoogte is donker lyne. Hieronder is nog drie voorbeelde van basis/hoogte-pare.
  • Trek met twee ander kleure die ander twee basis/hoogte-pare in elk van die boonste ses driehoeke, elke paar in sy eie kleur. Doen daarna die volgende oefening:

Kies een van die driehoeke en bereken sy oppervlakte drie keer. Meet die lengtes met jou liniaal en gebruik elke slag ‘n ander basis/hoogte-paar vir jou berekening. Stem die antwoorde grootliks ooreen? Indien nie, meet weer versigtig en doen weer die som.

Questions & Answers

what are the important of economic to accounting students with references
salihu Reply
Economics is important because it helps people understand how a variety of factors work with and against each other to control how resources such as labor and capital get used, and how inflation, supply, demand, interest rates and other factors determine how much you pay for goods and services.
Muhammad
explain the steps taken by the government in developing rural market?
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AS
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Amir
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Effah Reply
Pls, I need more explanation on price Elasticity of Supply
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Is the degree to the degree of responsiveness of a change in quantity supplied of goods to a change in price
Afran
Discuss the short-term and long-term balance positions of the firm in the monopoly market?
Rabindranath Reply
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Mitiku
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Rabindranath
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Umarou
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Anteyi Reply
A firm is a business entity which engages in the production of goods and aimed at making profit.
Avuwada
What is autarky in Economics.
Avuwada
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Tia Reply
So how is the perfect competition different from others
Rev Reply
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Tia
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Alfred Reply
1
Naziru
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Docky
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Docky
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Anna
The short run is a period of time in which the quantity of at least one inputs is fixed...
Anna
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Anna
Elacisity
salihu
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Suraj Reply
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Chinedum Reply
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babsnof
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eshita
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Suraj
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Mr
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babsnof
what is different between demand and supply
Debless Reply
Demand refers to the quantity of products that consumers are willing to purchase at various prices per time while Supply has to do with the quantity of products suppliers are willing to supply at various prices per time. find the difference in between
Saye
Please what are the effects of rationing Effect of black market Effects of hoarding
Atty Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
Mapo 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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