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Inleiding

Die doel van hierdie hoofstuk is om van die meetkundige en trigonometriese beginsels, wat jy in die verlede teëgekom het, te hersien. Jy moet gemaklik wees met die werk wat behandel word in dié hoofstuk voor jy die Graad 10 Meetkunde Hoofstuk of die Graad 10 Trigonometrie Hoofstuk aanpak. Die hoofstuk hersien die volgende:

  1. Terminologie: vierhoeke, hoekpunte, sye, hoeke, parallele lyne, loodregte lyne, hoeklyne, halveerlyne en snylyne
  2. Ooreenstemmings en verskille tussen driehoeke en vierhoeke
  3. Eienskappe van driehoeke en vierhoeke
  4. Kongruensie
  5. Onderskeid tussen skerphoeke, regte hoeke, stomphoeke, reguitlyne en 'n volle omwenteling
  6. Pythagoras se Teorie, wat gebruik word om die sye van reghoekige driehoeke se lengtes te bereken

Punte en lyne

Die twee eenvoudigste elemente in meetkunde is punte en lyne .

ʼn Punt is ʼn koördinaat wat ʼn posisie in ruimte aandui (óf op ʼn getallelyn, óf in ʼn vlak óf in ʼn drie- of meerdimensionele ruimte) en word voorgestel deur ʼn dot. Punte word gewoonlik aangedui met ʼn hoofletter. ʼn Paar voorbeelde van hoe punte aangedui word, kan gesien word in [link] .

ʼn Lyn is ʼn stel kontinue koördinate in ʼn ruimte en kan gesien word as baie punte wat langs mekaar is. Lyne kan reguit of geboë wees, maar is altyd kontinu en dus is daar geen onderbrekings in lyne nie. Die eindpunte van lynstukke word met hoofletters aangedui. Voorbeelde van twee lyne word in [link] aangetoon.

Voorbeelde van ʼn paar punte (aangedui deur P , Q , R en S ) en ʼn paar lyne (aangedui deur B C en D E )

ʼn Lyn word aangedui deur ʼn beginpunt en ʼn eindpunt. Ons noem ʼn lyn wat begin by punt A en eindig by punt B , A B . Aangsien die lyn van punt B tot punt A dieselfde is as as die lyn van punt A tot die punt B , kan ons sê dat A B = B A .

Die lengte tussen die punte A en B is A B . Dus as ons sê A B = C D word dit bedoel dat die lengte van die lynstuk tussen A en B gelyk is aan die lengte tussen C en D .

ʼn Lyn word gemeet in eenhede van lengte . ʼn Paar voorbeelde van algemene eenhede van lengte word gelys in [link] .

’n Paar algemene eenhede van lengte en hul afkortings
Eenheid van lengte Afkorting
kilometer km
meter m
sentimeter cm
millimeter mm

Hoeke

ʼn Hoek word gevorm as twee lyne in ʼn gemeenskaplike punt ontmoet. Die punt waar twee lyne ontmoet staan bekend as die hoekpunt . Hoeke word aangedui deur ʼn ^ (kappie) bo 'n letter te plaas. Byvoorbeeld, in [link] is daar 'n hoek by B ^ . Hoeke kan ook aangedui word met behulp van die lyn segmente waaruit die hoek bestaan. Byvoorbeeld, in [link] word die hoek gevorm waar die lynsegmente C B en B A mekaar ontmoet. Die hoek kan dus aangedui word deur C B A of A B C . Die simbool dui 'n hoek in meetkunde aan.

Hoeke word gemeet in grade wat aangedui word deur die simbool (byvoorbeeld, 60 ).

Hoeke kan ook gemeet word in radiale. In die hoërskool sal ons slegs grade gebruik, maar in wiskunde op universiteitsvlak sal jy definitief weer radiale teëkom.

Hoek aangedui deur B ^ , C B A of A B C
Voorbeelde van hoeke. A ^ = E ^ , al is die lyne wat die verskillende hoeke vorm van verskillende lengtes

Meting van hoeke

Die grootte van ʼn hoek is onafhanklik van die lengtes van die twee sye wat die hoek onderspan. Dit hang slegs af van hoe die twee lyne relatief tot mekaar geplaas word, soos aangedui in [link] . ʼn Hoek vorm wanneer daar geroteer word om ʼn hoekpunt.

Questions & Answers

find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
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
Abhi
how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
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
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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