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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.

Exercise 1: Bewyse - 1

Gegee vierhoek ABCD, met AB∥CDAB∥CD en AD∥BCAD∥BC, bewys dat B A ^ D = B C ^ A B A ^ D= B C ^ A en A B ^ C = A D ^ C A B ^ C= A D ^ C.

[ Show Solution ]

Proofs - 2 2

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

Figure 2
Figure 2 (geomproof2.png)
Dit word ook gegee dat AB=CDAB=CD, AD=BCAD=BC, AB∥CDAB∥CD, AD∥BCAD∥BC, A ^ = C ^ A ^ = C ^ , en B ^ = D ^ B ^ = D ^ . Bewys dat MNOP parallelogram is.

[ Show Solution ]

Warning:

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!

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