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MULO-A Meetkunde 1907 Algemeen

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(1)

Uitwerkingen Meetkunde MULO-A 1907 (

1 2 1

uur)

Opgave 1.

In BDC kunnen we CD met behulp van Pythagoras uitrekenen. Dit geeft 1

2 3 CDa . 1 2 1 6 1 3 AD a DE a AE a       .

In CDE vinden we met de stelling van Pythagoras

 

2

2 2 2 2 1 1 2 6 2 3 DECDCEaaCE  2 1 2 3 2 28 2 7 2 36 4 36 9 CEaaaa  2 7 1 9 3 7 CEaa .

Opgave 2.

Omdat ESDABD geldt

: :

ES AB ED AD (a). Omdat SFC ABC geldt

: :

SF AB FC BC (b).

Vanwege AB EF CD// // geldt

: :

ED AD FC BC (c).

Uit (a), (b) en (c) volgt:

: : : : : : : : ES AB ED AD SF AB FC BC ES AB SF AB ES SF ED AD FC BC          

Opgave 3.

Uitgaande van een gelijkzijdige driehoek ABC kunnen we behulp van een bissectrice

achtereenvolgens de hoeken DCB30o , o 15 DCE   , FCB7 30 'o , GCB3 45'o

tekenen en de hoeken DCE en GCB bij elkaar optellen tot GCH 18 45'o

( o o 3 45' 15 ).

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