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Bewyse en vermoedens in meetkunde

Jy het gesien hoe om meetkunde en die eienskappe van poligone te gebruik om die onbekende lengtes van sye en die groottes van hoeke van verskeie vierhoeke en poligone te vind. Ons gaan nou hierdie werk uitbrei om sommige van die eienskappe te bewys en probleme op te los. ʼn Vermoede is ʼn wiskundige se manier om te se: "Ek glo dit is waar, maar ek het geen bewys nie". Die volgende uitgewerkte voorbeelde sal help om dit duideliker te maak.

Gegee vierhoek ABCD, met A B C D en A D B C , bewys dat B A ^ D = B C ^ A en A B ^ C = A D ^ C .

  1. Ons maak die volgende skets en trek die diagonale.
  2. Gegee: A B C D en A D B C . Ons moet bewys A = C en B = D . In formele wiskundetaal sê ons dat ons gevra word om te bewys (RTP='requested to prove'): B A ^ D = B C ^ A en A B ^ C = A D ^ C .
  3. B A ^ C = A C ^ D ( verwisselende binnehoeke ) D A ^ C = B C ^ A ( verwisselende binnehoeke ) B A ^ D = B C ^ A
    Net so vind ons dat:
    A B ^ C = A D ^ C

In parallelogram ABCD, is die halveerlyne van die hoeke (AW, BX, CY en DZ) gekonstrueer:

Dit word ook gegee dat AB = CD , AD = BC , AB CD , AD BC , A ^ = C ^ , en B ^ = D ^ . Bewys dat MNOP parallelogram is.

  1. Gegee: AB = CD , AD = BC , AB CD , AD BC , A ^ = C ^ , and B ^ = D ^ . Bewys MNOP is ʼn parallelogram.
  2. In ADW and CBY D A ^ W = B C ^ Y ( gegee ) A D ^ C = A B ^ C ( gegee ) AD = BC (gegee) ADW = CBY (HHS) DW = BY
    In ABX and CDZ D C ^ Z = B A ^ X ( gegee ) Z D ^ C = X B ^ A ( gegee ) DC = AB (gegee) ABX CDZ (HHS) AX = CZ
    In XAM and ZCO X A ^ M = Z C ^ O ( gegee ) A X ^ M = C Z ^ O ( reeds bewys ) AX = CZ (reeds bewys) XAM COZ (HHS) A O ^ C = A M ^ X
    A M ^ X = P M ^ N (regoorstaande hoeke) C O ^ Z = N O ^ P (regoorstaande hoeke) P M ^ N = N O ^ P
    In BYN and DWP Y B ^ N = W D ^ P ( gegee ) B Y ^ N = W D ^ P ( reeds bewys ) DW = BY (reeds bewys) YBN WDP (AAS) B N ^ Y = D P ^ W
    D P ^ W = M P ^ O (regoorstaande hoeke) B N ^ Y = O N ^ M (regoorstaande hoeke) M P ^ O = O N ^ M

    MNOP is ʼn parallelogram (beide pare teenoorstaande 'e = , daarom is beide pare teenoorstaande sye ook parallel)

Dit is baie belangrik om daarop te let dat ʼn enkele teen-voorbeeld genoeg is om ʼn vermoede verkeerd te bewys. Selfs ʼn menigte ondersteunende voorbeelde is nog steeds geen bewys nie!

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, 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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