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Graad 9

Vierkante, perspektieftekening, transformasies

Module 22

Vergelyking van vierhoeke ten opsigte van verskille en ooreenkomste


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.


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

Need help solving this problem (2/7)^-2
Simone Reply
what is the coefficient of -4×
Mehri Reply
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
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lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
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I'm 13 and I understand it great
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
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okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
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Commplementary angles
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
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How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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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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