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Wiskunde

Grade 8

Verhoudings en eweredigheid

Meting en vormleer

Konstruksies

Module 17

Konstruksie van verskillende soorte hoeke

AKTIWITEIT 1

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:

  • A B ˆ size 12{ { hat {B}}} {} C = 75°

Soort hoek: ______

2.2 C D ˆ size 12{ { hat {D}}} {} E = 135°

Soort hoek: ______

2.3 F G ˆ size 12{ { hat {G}}} {} H = 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 Δ size 12{Δ} {} ABC met BC = 40 mm, B ˆ size 12{ { hat {B}}} {} = 70° en C ˆ size 12{ { hat {C}}} {} = 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 Δ size 12{Δ} {} PQR met QR = 58 mm, P Q ˆ size 12{ { hat {Q}}} {} R = 62° en Q P ˆ size 12{ { hat {P}}} {} R = 69°.

Meet:

  1. PQ = mm
  2. R ˆ size 12{ { hat {R}}} {} =

4.2 Gelykbenige Δ size 12{Δ} {} ABC met BC = 42 mm, AB = AC en B ˆ size 12{ { hat {B}}} {} = 63°.

Meet:

a) PQ = mm

AKTIWITEIT 2

Om enige gegewe lyn of hoek te halveer [LU 3.4, 3.5, 4.7]

  1. 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 B ˆ size 12{ { hat {B}}} {} (hoek B ) met die plek waar jou “kapmerke” mekaar kruis.
  • B ˆ size 12{ { hat {B}}} {} 1 sal nou net so groot wees soos B ˆ size 12{ { hat {B}}} {} 2 . Meet beide hoeke. Is hulle ewe groot?

4. Probeer nou self die volgende doen:

  • Teken D E ˆ size 12{ { hat {E}}} {} F . = 125°.
  • Halveer nou D E ˆ size 12{ { hat {E}}} {} F .

AKTIWITEIT 3

Om ‘n loodlyn vanuit ‘n punt op ‘n lyn te konstrueer [LU 3.4, 3.5, 4.7]

1. Konstrueer AD size 12{ ortho } {} BC .

  • 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 . ( AD size 12{ ortho } {} BC .)

Questions & Answers

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Winnerman Reply
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SHAH Reply
the situation in which elements of monopoly ( R&D, EOS and stability of prices etc.) allow individual producers or consumers to exercise some control over market prices
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Ayedun
Micro-economics refers to the branch of economics which deals with smaller unit or element of the economy.
Amadu
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Neriel
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financial intermediaries are those who are link between borrowers and lenders for.eg bank... Bank is a financial intermediary
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Toyin
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Toyin
law of diminishing utility...as the quantity consumed of a commodity increases,the utility derived from each successive unit goes on decreasing... condition___ consumption of other commodities remaining the same.
Malik
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Malik
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Amos
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Survival Reply
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Md
There is an inverse relation between price and the quantity demanded...with the increase in price of a commodity, the demand for the commodity decreases and vice versa..
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as the science that studies human behavior as the relationship between earn and scarce means which has alternative uses
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Suqlain
Difference between extinct and extici spicies
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Source:  OpenStax, Wiskunde graad 8. OpenStax CNX. Sep 11, 2009 Download for free at http://cnx.org/content/col11033/1.1
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