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Vierkant

ʼn Vierkant is ʼn rombus met al vier sye ewe lank en al vier hoeke gelyk aan 90 .

ʼn Opsomming van die eienskappe van ʼn vierkant:

  • Beide pare teenoorstaande sye is parallel.
  • Al vier sye is ewe lank.
  • Al vier die hoeke is 90 .
  • Beide pare teenoorstaande hoeke is ewe groot.
  • Die hoeklyne halveer mekaar met hoeke van 90 .
  • Diagonale is ewe lank.
  • Diagonale halveer beide pare teenoorstaande hoeke (d.w.s. hulle is almal 45 ).
ʼn Voorbeeld van ʼn vierkant - ʼn rombus met al die hoeke gelyk aan 90

Vlieër

ʼn Vlieër is ʼn vierhoek met twee pare aangrensende sye ewe lank.

ʼn Oposmming van die eienskappe van ʼn vlieër is:

  • Twee pare aangrensende sye is ewe lank.
  • Een paar teenoorstaande hoeke (die hoeke tussen die ongelyke sye) is ewe groot.
  • Een diagonaal halveer die ander een en hierdie diagonaal halveer ook een paar teenoorstaande hoeke.
  • Diagonale sny mekaar reghoekig.
ʼn Voorbeeld van ʼn vlieër

Reghoeke is ʼn spesiale geval (ʼn deelversameling) van die parallelogramme. Reghoeke is parallelogramme met alle hoeke regte hoeke. Vierkante is ʼn spesiale geval (deelversameling) van die reghoeke. Vierkante is reghoeke met al vier sye ewe lank. So, alle vierkante is parallelogramme én reghoeke. As jy gevra word om te bewys dat ʼn vierhoek ʼn parallelogram is, is dit genoeg om aan te toon dat beide pare teenoorstaande sye parallel is. Maar, as jy gevra word om te bewys dat ʼn vierhoek ʼn vierkant is, dan moet jy ook wys dat al die hoeke regte hoeke is én dat al die sye ewe lank is.

Veelhoeke

Veelhoeke is oral rondom ons. ʼn Stopteken het die vorm van ʼn agthoek, m.a.w. ʼn agthoekige veelhoek. Die heuningkoek van ʼn bynes bestaan uit heksagonale selle. Die oppervlak van ʼn tafel is dikwels ʼn reghoek.

In hierdie afdeling sal jy leer van gelykvormige veelhoeke.

Gelykvormigheid tussen veelhoeke

Bespreking: gelykvormige driehoeke

Gebruik die diagram om die tabel in te vul en beantwoord die vrae wat daarop volg.

AB DE = . . . c m . . . c m = . . . A ^ =... D ^ ...
BC EF = . . . c m . . . c m = . . . B ^ =... E ^ =...
AC DF = . . . c m . . . c m = . . . C ^ ... F ^ =...

  1. Wat kan jy sê oor jou berekening van: AB DE , BC EF , AC DF ?
  2. Wat kan jy sê oor A ^ en D ^ ?
  3. Wat kan jy sê oor B ^ en E ^ ?
  4. Wat kan jy sê oor C ^ en F ^ ?

As twee veelhoeke gelykvormig is, is die een ʼn vergroting van die ander. Dit beteken dat die veelhoeke dieselfde grootte hoeke sal hê en dat hulle sye in verhouding tot mekaar sal wees.

Die simbool wat ons gebruik om gelykvormigheid aan te dui is ||| .

Gelykvormige Veelhoeke

Twee veelhoeke is gelykvormig as:

  1. hulle ooreenstemmende hoeke ewe groot is, én
  2. hulle ooreenstemmende sye eweredig is (die verhouding van die sylengtes gelyk is.)

Bewys dat die volgende twee veelhoeke gelykvormig is.

  1. Daar word gevra om te bewys dat ʼn paar veelhoeke gelykvormig is. Ons kan dit doen deur te bewys dat die verhouding van ooreenstemmende sye gelyk is en dat die ooreenstemmende hoeke ewe groot is.

  2. Die hoeke en hul groottes word gegee, so ons kan bewys dat hulle ewe groot is.

  3. Al die hoeke is 90 groot en

    A ^ = E ^ B ^ = F ^ C ^ = G ^ D ^ = H ^
  4. Eerstens moet ons kyk watter sye ooreenstem. Die reghoeke het twee lang sye wat gelyk is en twee kort sye wat gelyk is. Ons moet die verhoudings van die lang sye van die twee reghoeke vergelyk en ons moet die verhoudings van die kort sye vergelyk.

    Lang sye, groot reghoek se waardes op die klein reghoek se waardes:

    Verhouding = 2 L L = 2

    Kort sye, groot reghoek se waardes op die klein reghoek se waardes:

    Verhouding = L 1 2 L = 1 1 2 = 2

    Die verhouding van die ooreenstemmende sye is gelyk, twee in hierdie geval.

  5. Die ooreenstemmende hoeke is ewe groot en die verhoudings van die ooreenstemmende sye is gelyk, dus is dieveelhoeke ABCD en EFGH gelykvormig.

Alle vierkante is gelykvormig.

As twee vyfhoeke ABCDE en GHJKL gelykvormig is, bepaal die lengtes van die sye en die groottes van die hoeke wat met letters gemerk is:

  1. Daar word aan ons gegee dat ABCDE en GHJKL gelykvormig is. Dit beteken dat:

    AB GH = BC HJ = CD JK = DE KL = EA LG

    en

    A ^ = G ^ B ^ = H ^ C ^ = J ^ D ^ = K ^ E ^ = L ^
  2. Daar word gevra om te bepaal

    1. a , b , c en d , en
    2. e , f and g .
  3. Die ooreenstemmende hoeke is ewe groot en daar is dus geen berekening nodig nie. Daar word aan ons ʼn paar sye D C en K J gegee wat ooreenstemmend is. D C K J = 4 , 5 3 = 1 , 5 so ons weet dat al die sye van K J H G L 1,5 keer kleiner is as die sylengtes van A B C D E .

  4. a 2 = 1 , 5 a = 2 × 1 , 5 = 3 b 1 , 5 = 1 , 5 b = 1 , 5 × 1 , 5 = 2 , 25 6 c = 1 , 5 c = 6 ÷ 1 , 5 = 4 d = 3 1 , 5 d = 2
  5. e = 92 ( ooreenstemmend tot H ) f = 120 ( ooreenstemmend tot D ) g = 40 ( ooreenstemmend tot E )
  6. a = 3 b = 2 , 25 c = 4 d = 2 e = 92 f = 120 g = 40

Gelykvormigheid van gelyksydige driehoeke

Werk in pare en toon dat alle gelyksydige driehoeke gelykvormig is.

Veelhoeke gemeng

  1. Vind die onbekende waardes in elke geval. Gee redes.
  2. Vind die hoeke en lengtes wat met letters gemerk is in die volgende figure:

Ondersoek: definieer poligone

Ondersoek verskillende maniere om poligone te definieer. Jy behoort spesiale aandag te gee aan die volgende poligone:

  • Gelykbenige driehoeke, gelyksydige driehoeke, reghoekige driehoeke
  • Vlieërs, parallelogramme, reghoeke, rombusse, vierkante, trapesiums

Neem in oorweging hoe die figure in hierdie boek gedefinieer is en watter alternatiewe definisies daar bestaan. Byvoorbeeld, ʼn driehoek is ʼn driesydige poligoon of ʼn driehoek is ʼn figuur met drie sye en drie hoeke. Driehoeke kan geklassifiseer word volgende hulle sye of volgens hulle hoeke. Kan mens ook vierhoeke op hierdie manier klassifiseer? Watter ander name is daar vir hierdie figure? Byvoorbeeld, vierhoeke kan ook genoem word tetragone.

Questions & Answers

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
Commplementary angles
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a perfect square v²+2v+_
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algebra 2 Inequalities:If equation 2 = 0 it is an open set?
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or infinite solutions?
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Kristine 2*2*2=8
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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J, combine like terms 7x-4y
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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.
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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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