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Samenvatting Getal & Ruimte 12e ed 3 vwo uitwerkingen deel 1 H2
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Getal & Ruimte 12e ed 3 vwo uitwerkingen deel 1 Hoofdstuk 2: Gelijkvormigheid
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UITWERKINGENDEEL 1
WISKUNDE 12e EDITIE
3 VWO
,Getal & Ruimte
Uitwerkingen
3 vwo deel 1
Twaalfde editie, 2019 Auteurs
Noordhoff J. H. Dijkhuis
Groningen C. J. Admiraal
J. A. Verbeek
G. de Jong
H. J. Houwing
J. D. Kuis
F. ten Klooster
S. K. A. de Waal
J. van Braak
J. H. M. Liesting-Maas
M. Wieringa
M. L. M. van Maarseveen
R. D. Hiele
J. E. Romkes
M. Haneveld
S. Voets
I. Cornelisse
M. Vos
B.W. van Laarhoven
, 2 Gelijkvormigheid
Voorkennis Berekeningen in driehoeken
Bladzijde 54
1 In -ABC is ∠C = 90°, dus AC2 + BC2 = AB2
52 + 22 = AB2
AB2 = 25 + 4 = 29
AB = 冑29 ≈ 5,39 cm
In -DEF is ∠D = 90°, dus DE2 + DF2 = EF2
DE2 + 32 = 5,82
DE2 = 33,64 − 9 = 24,64
DE = 冑24,64 ≈ 4,96 cm
In -QRS is ∠S = 90°, dus QS2 + RS2 = QR2
QS2 + 42 = 4,62
QS2 = 21,16 − 16 = 5,16
QS = 冑5,16 = 2,271...
Dus PQ = 2 · 2,271... ≈ 4,54 cm
Bladzijde 55
2 a Zie de figuur hiernaast. Q
∠R = 90°, dus PR2 + QR2 = PQ2
7,22 + QR2 = 8,32 8,3
QR2 = 68,89 − 51,84 = 17,05
QR = 冑17,05 ≈ 4,13 cm
P R
7,2
b Zie de figuur hiernaast. D C
In -ABC is ∠B = 90°, dus AB2 + BC2 = AC2
62 + 42 = AC2
4
AC2 = 36 + 16 = 52
AC = 冑52 ≈ 7,21 cm
Dus elke diagonaal is 7,21 cm. A 6 B
c Zie de figuur hiernaast. E
In -EFG is ∠G = 90°, dus EG2 + FG2 = EF2
EG2 + 4,52 = 72
EG2 = 49 − 20,25 = 28,75 7 7
EG = 冑28,75 ≈ 5,36 cm
Dus de hoogte die bij zijde DF hoort is 5,36 cm.
D F
4,5 G 4,5
3 a ∠C1 = ∠C2 = 105° (overstaande hoeken)
∠B = ∠E = 46° (Z-hoeken)
∠A = 180° − 105° − 46° = 29° (hoekensom driehoek)
b ∠P = 180° − 82° − 31° = 67° (hoekensom driehoek)
∠T1 = ∠Q = 31° (F-hoeken)
∠T2 = 180° − 31° = 149° (gestrekte hoek)
4 a ∠K = ∠L1 = 32° (basishoeken)
∠M = 180° − 90° − 32° = 58° (hoekensom driehoek)
∠N1 = 180° − 32° − 32° = 116° (hoekensom driehoek)
∠N2 = 180° − 116° = 64° (gestrekte hoek)
b ∠A12 = ∠B3 = 68° (F-hoeken)
∠D1 = 180° − 32° − 68° = 80° (hoekensom driehoek)
∠A1 = 68° − 38° = 30°
∠C2 = ∠A1 = 30° (Z-hoeken)
∠S1 = 180° − 32° − 30° = 118° (hoekensom driehoek)
∠S2 = 180° − 118° = 62° (gestrekte hoek)
44 Hoofdstuk 2 © Noordhoff Uitgevers bv
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