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Hoe om 'n gradeboog te gebruik

ʼn Gradeboog is ʼn eenvoudige instrument wat gebruik word om hoeke te meet. ʼn Diagram van ʼn gradeboog word getoon in [link] .

Diagram van 'n gradeboog

Metode:

Hoe om 'n gradeboog te gebruik:

  1. Plaas die onderste lyn van die gradeboog langs een van die sye van die hoek. Die tweede lyn moet in die rigting van die afgemete skaal wys.
  2. Beweeg die gradeboog sodat die middelpunt van die gradeboog en die hoekpunt oorstem.
  3. Lees af waar die tweede lyn van die hoek die afgemete skaal kruis. Maak seker dat jy by die 0 begin lees.

Meting van hoeke: gebruik ʼn gradeboog om die volgende hoeke te meet

Spesiale hoeke

Wat is die kleinste hoek wat geteken kan word? Die figuur hier onder toon aan hoe twee lyne ( C A en A B ) ʼn hoek onderspan by die hoekpunt A . As die lyn C A geroteer word om die hoekpunt A , in die rigting van lyn A B , dan is die kleinste hoek wat geteken kan word, die geval waar beide lyne in dieselfde rigting wys. Dit noem ons ʼn 0 hoek. Dit word aangedui in [link] .

As lyn C A nou opwaarts geroteer word, kan enige ander hoek gevorm word. As lyn C A en lyn A B in presies teenoorgestelde rigtings wys (soos in geval 3 in [link] ) word ʼn 180 hoek onderspan.

As drie punte A , B en C op ʼn reguitlyn lê, is die hoek wat onderspan word 180 . Netso, as die hoek tussen 3 punte 180 is, lê die punte op ʼn reguitlyn.

ʼn Hoek van 90 word ʼn regte hoek genoem. ʼn Regte hoek is die helfte van die hoek wat onderspan word deur die reguitlyn (die 180 lyn). Ons sê dus C A is loodreg op A B of C A A B . ʼn Hoek, twee maal die grootte van die hoek wat die reguitlyn onderspan, is 360 . ʼn Hoek van 360 is presies dieselfde as ʼn 0 , hoek (behalwe vir die notasie). Ons noem dit 'n omwenteling .

'n Hoek van 90 word aangedui as 'n regte hoek .

Hoeke groter as 360

Alle hoeke, groter as 360 , lyk dieselfde as hoeke wat ons alreeds teëgekom het. As jy ʼn hoek gegee word wat groter is as 360 , trek 360 herhaaldelik af van die hoek, tot jy 'n antwoord kry tussen 0 and 360 . Hoeke wat meer as 360 is meestal vir die wiskundige gerief.

  • Skerphoek : 'n Hoek 0 en < 90 .
  • Regtehoek : 'n Hoek gelyk aan 90 .
  • Stomphoek : 'n Hoek > 90 en < 180 .
  • Reguitlynhoek : 'n Hoek gelyk aan 180 .
  • Inspringende hoek : 'n Hoek > 180 en < 360 .
  • Omwenteling : 'n Hoek gelyk aan 360 .

Hierdie is basies net name vir hoeke in ‘n spesifieke reeks, soos gewys in [link] .

Drie soorte hoeke

Waneer jy hoeke meet, kan jy hulle met mekaar vergelyk. Byvoorbeeld, alle regte hoeke is 90 , dus is alle regte hoeke is gelyk aan mekaar en ‘n stomphoek sal altyd groter wees as ‘n skerphoek.

Die volgende video gee ‘n opsomming van wat jy moet weet van hoeke.

Khan akademie video oor hoeke - 1

Let daarop dat vir hoërskool sal jy net grade gebruik, nie radiale soos gewys in die video nie. Radiale is ‘n ander manier om hoeke te meet. Jy sal op universiteit aan radiale voorgestel word.

Spesiale hoekpare

In [link] , sny reguitlyne A B en C D in punt X en dit vorm vier hoeke: X 1 ^ of B X D , X 2 ^ of B X C , X 3 ^ of C X A en X 4 ^ of A X D .

Twee kruisende reguitlyne vorm hoeke X 1 ^ , X 3 ^ en X 2 ^ , X 4 ^ .

Die tabel gee ‘n opsomming van spesiale hoekpare.

Spesiale Hoeke Eienskap Byvoorbeeld
Aangrensende hoeke deel ‘n hoekpunt en 'n gemeenskaplike sy ( X 1 ^ , X 2 ^ ) , ( X 2 ^ , X 3 ^ ) , ( X 3 ^ , X 4 ^ ) , ( X 4 ^ , X 1 ^ )
Lineêre paar (aangrensende hoeke op ‘n reguitlyn) aangrensende hoeke wat gevorm word by twee snydende reguitlyne wat volgens definisie saam 180 is X 1 ^ + X 2 ^ = 180 ; X 2 ^ + X 3 ^ = 180 ; X 3 ^ + X 4 ^ = 180 ; X 4 ^ + X 1 ^ = 180
Teenoorstaande hoeke hoeke wat gevorm word deur 2 snydende reguitlyne wat ‘n hoekpunt deel maar nie enige sye nie X 1 ^ = X 3 ^ ; X 2 ^ = X 4 ^
Supplementêre hoeke 2 hoeke waarvan die som 180 is
Komplementêre hoeke 2 hoeke waarvan die som 90 is

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Source:  OpenStax, Siyavula textbooks: wiskunde (graad 10) [caps]. OpenStax CNX. Aug 04, 2011 Download for free at http://cnx.org/content/col11328/1.4
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