Om verskillende soorte hoeke en driehoeke te konstrueer
[LU 3.4, 3.5, 4.7]
1. Hoe om ‘n hoek te teken:Benodigdhede: potlood, liniaal, gradeboog.
1.1 Begin altyd met ‘n basislyn.
1.2 Maak ‘n merkie vir ‘n begin bv. links en plaas jou gradeboog op jou merkie.
1.3 Lees óf van die buitekant óf die binnekant van jou gradeboog vanaf 0°.
1.4 By hoeke groter as 180° moet jy eers die bepaalde hoek van 360° aftrek, en dan daardie betrokke hoek teken. Die hoek buitekant om (die inspringende hoek) sal dan die betrokke hoek wees wat jy moet teken.Bv. 320°: (360° – 320° = 40°). Teken nou ‘n hoek van 40°. Die inspringende hoek verteenwoordig nou die 320°.
2. Konstrueer nou die volgende hoeke en benoem elke hoek:
AC = 75°
Soort hoek:______
2.2
CE = 135°
Soort hoek:______
2.3
FH = 215°
Soort hoek:______
3. Hoe om ‘n driehoek te konstrueer:
Benodigdhede: potlood, liniaal, gradeboog en passer.
Begin altyd eers deur ‘n rowwe skets te maak.
Gebruik dan een van die sye waarvan die lengte gegee is, as basis.
Bv. konstrueer
ABC met
BC = 40 mm,
= 70° en
= 50°.
Rowwe skets:
Om ‘n sylengte akkuraat te meet moet jy die lengte met jou passer op jou liniaal meet en dan jou passer se punt op
B sit en met die potlood ‘n “kapmerk” maak waar
C moet wees.
Konstruksie:
4. Konstrueer nou elk van die volgende driehoeke:
4.2
PQR met
QR = 58 mm,
PR = 62° en
QR = 69°.
Meet:
PQ = mm
=
4.2 Gelykbenige
ABC met
BC = 42 mm,
AB =
AC en
= 63°.
Meet:
a) PQ = mm
AKTIWITEIT 2
Om enige gegewe lyn of hoek te halveer [LU 3.4, 3.5, 4.7]
Halvering van ‘n gegewe lyn
AB :
Meet lynstuk
AB (bv. 40 mm).
Neem jou passer en meet bietjie meer as die helfte van jou lyn (d.w.s. ± 22-25 mm).
Plaas jou passer se skerppunt op
A en maak ‘n “kapmerk” onder en bo die lyn.
Plaas dan jou passer op
B en maak ook ‘n “kapmerk” bo en onder die lyn.
Verbind die kruispunte van die twee “kapmerke” met mekaar.
Benoem die punt op lyn
AB ,
P. P is nou die middelpunt van lyn
AB .
2. Probeer nou self die volgende:
Teken ‘n lynstuk
PQ = 70 mm.
Halveer nou lynstuk
PQ , soos in nr. 1 verduidelik.
3. Halvering van π
ABC :
Plaas jou passer se skerppunt op
B .
Trek enige grootte boog soos aangedui.
Plaas jou passer se punt op die punt waar die twee lyne mekaar kruis en maak ‘n “kapmerk” binne die hoek.
Plaas nou jou passer se punt op die ander punt waar die twee lyne mekaar kruis en maak ‘n “kapmerk” binne die hoek, sodat jou twee “kapmerke” mekaar kruis.
Verbind
(hoek
B ) met die plek waar jou “kapmerke” mekaar kruis.
1 sal nou net so groot wees soos
2 . Meet beide hoeke. Is hulle ewe groot?
4. Probeer nou self die volgende doen:
Teken
DF . = 125°.
Halveer nou
DF .
AKTIWITEIT 3
Om ‘n loodlyn vanuit ‘n punt op ‘n lyn te konstrueer [LU 3.4, 3.5, 4.7]
1. Konstrueer
ADBC .
Plaas jou passer se skerppunt op
A (want jy wil uit
A ‘n lyn loodreg op
BC trek.)
Maak nou ‘n boog op
BC .
Plaas jou passer se punt eers op die een punt waar die boog en
BC mekaar kruis en maak ‘n “kapmerk” onder
BC en dan op die ander kruispunt en maak weer ‘n “kapmerk” onder
BC , sodat jou twee “kapmerke” mekaar kruis.
Verbind nou
A met die kruispunt van die twee “kapmerke”.
Merk die plek waar die twee lyne mekaar sny,
D .
AD is nou loodreg op
BC . (
ADBC .)
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