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2.1 Meetkunde van lyne en driehoeke

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Wiskunde

Graad 9

Algebra en meetkunde

Module 8

Meetkunde van lyne en driehoeke

Meetkunde van lyne en driehoeke

Aktiwiteit 1

Om die gebruiklike benoeming van sye en hoeke in driehoeke te leer

Verwys na die driehoek om die terme te verstaan.Die drie sye van die driehoek is AB, AD en BD.‘n Sy in ‘n driehoek kan ook die naam van die oorstaande hoek as ‘n kleinletter kry. Die hoeke (vertekse) word met hoofletters geskryf. As A of A ˆ size 12{ { hat {A}}} {} gebruik word, verwys dit na die hoek wat sye BA en AD vorm. Ons kan die hoek ook BAD of B A ˆ D size 12{B { hat {A}}D} {} noem. En as ek A=38° gebruik, is dit duidelik wat ek bedoel. Ons benoem die driehoek ABD of ΔABD, met die letters in alfabetiese orde.

Oefening:

Teken die volgende tekening in die spasie

regs, om te wys dat jy begryp hoe die beskrywings

gebruik word:

Teken ΔQRT met q=4cm, T=65° en QT=5,5cm.

Sien jy dat dit nie nodig is om die lengte van t,

of die groottes van Q ˆ size 12{ { hat {Q}}} {} of R ˆ size 12{ { hat {R}}} {} te weet nie? Maak eers

‘n rowwe skets om jou te help om jou werk te

beplan.

Opdrag:

Jy weet alreeds dat driehoeke volgens hulle vorm geklassifiseer word. Maak ‘n A4–grootte plakkaat vir jouself waarop die eienskappe van die volgende soorte driehoeke duidelik aangetoon word: gelyksydig, reghoekig, gelykbenig en ongelyksydig. Benoem die hoeke en sye soos hierbo verduidelik. Werk so noukeurig en netjies as moontlik.

Meet die sye en hoeke van jou driehoeke en vul dit in op die plakkaat.

Aktiwiteit 2

Om die beginsel van kongruensie in driehoeke te ondersoek

[LU 4.4, 3.3, 3.5]

In die vorige oefening het jy ΔQTR volgens gegewe spesifikasies geteken. Vra die ander leerders wat hierdie oefening gedoen het om jou hulle sketse te wys, en bevestig dat hulle mates perfek ooreenstem met dié wat gegee is. Meet nou die sy en twee hoeke wat nie gegee is nie om te sien of hulle met joune ooreenstem.

  • Almal se driehoeke wat volgens die spesifikasies getrek is, is altyd eenders. Inderwaarheid is dit onmoontlik om die driehoek korrek te teken sodat dit verskil! Skryf (met jou maat) neer presies hoekom dit so is.
  • Hier volg nog beskrywings van driehoeke. Werk hulle ook soos ΔQTR? Met ander woorde, is dit ook onmoontlik om verskillende driehoeke te teken? Skryf weer jou siening van die situasie neer. Die laaste een is moeilik om te teken – probeer gerus!
  • Teken ΔAGE met a=4cm, E=90° en AG=5cm.
  • Teken ΔNOH met HN=4cm, H=56° en O=72°.
  • Teken ΔBAT met B=48°, T=65° en A=67°.
  • Teken ΔMOD met m=5,5cm, O=65° en DM=4cm.
  • Teken ΔAMP met a=4,2cm, m=5cm en p=5,6cm.
  • In al die driehoeke hierbo spesifiseer ons net drie van die ses moontlike mates (drie sye en drie hoeke). Partykeer was dit genoeg om te verseker dat almal identiese driehoeke sou teken. Maar in ΔBAT en ΔMOD was die drie mates nie genoeg om identiese driehoeke van almal te verseker nie.
  • So, wanneer is drie genoeg? Dalk het jy alreeds die geheim uitgedink:

ΔQRT: Twee sye en die hoek tussen hulle is gegee.

ΔAGE: ‘n Regte hoek, die skuinssy en nog ‘n sy is gegee.

ΔNOH: Een sy en twee hoeke is gegee.

ΔAMP: Drie sye is gegee.

ΔBAT: Drie hoeke is gegee, maar daar is niks gesê van die driehoek se grootte nie!

Questions & Answers

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physiological Psychology
Nwosu Reply
How can I develope my cognitive domain
Amanyire Reply
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Dakolo Reply
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
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namakula Reply
Skinner skipped the whole unconscious phenomenon and rather emphasized on classical conditioning
war
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Jonathan
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interpersonal relationships
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Source:  OpenStax, Wiskunde graad 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11055/1.1
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