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[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Meld aan</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Bladsye vir uitgemelde redakteurs <a href="/wiki/Hulp:Inleiding" aria-label="Leer meer oor redigering"><span>leer meer</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spesiaal:Mybydrae" title="A list of edits made from this IP address [y]" accesskey="y"><span>Bydraes</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spesiaal:Mybespreking" title="Bespreking oor bydraes van hierdie IP-adres [n]" accesskey="n"><span>Bespreking</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Werf"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Inhoud" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Inhoud</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">versteek</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inleiding</div> </a> </li> <li id="toc-Begrip_van_'n_hoek" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Begrip_van_'n_hoek"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Begrip van 'n hoek</span> </div> </a> <ul id="toc-Begrip_van_'n_hoek-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Grootte_van_'n_hoek:_Graad" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Grootte_van_'n_hoek:_Graad"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Grootte van 'n hoek: Graad</span> </div> </a> <ul id="toc-Grootte_van_'n_hoek:_Graad-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Inhoud" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Wissel die inhoudsopgawe" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Wissel die inhoudsopgawe</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Meetkundige begrippe</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Hierdie artikel bestaan slegs in hierdie taal. 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class="vector-appearance-landmark" aria-label="Voorkoms"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Voorkoms</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">skuif na kantbalk</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">versteek</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">in Wikipedia, die vrye ensiklopedie</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="af" dir="ltr"><p>Die volgende artikel bespreek die onderskeie belangrike begrippe in die <a href="/wiki/Meetkunde" title="Meetkunde">meetkundige</a> veld van <a href="/wiki/Wiskunde" title="Wiskunde">wiskunde</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Begrip_van_'n_hoek"><span id="Begrip_van_.27n_hoek"></span>Begrip van 'n hoek</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkundige_begrippe&veaction=edit&section=1" title="Wysig afdeling: Begrip van 'n hoek" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkundige_begrippe&action=edit&section=1" title="Edit section's source code: Begrip van 'n hoek"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In die alledaagse lewe het ons al baie met hoeke kennis gemaak. Dink maar aan die hoek van 'n tafel, die hoek van 'n huis, die hoek van 'n vel papier ens. Wat is 'n hoek nou eintlik? In wiskunde beskou ons 'n hoek as die hoeveelheid draaiing wat 'n lyn om 'n vaste punt maak. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Hoeke_voorbeelde.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Hoeke_voorbeelde.png/220px-Hoeke_voorbeelde.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Hoeke_voorbeelde.png/330px-Hoeke_voorbeelde.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4d/Hoeke_voorbeelde.png/440px-Hoeke_voorbeelde.png 2x" data-file-width="639" data-file-height="359" /></a><figcaption></figcaption></figure> <p>Die twee figure hierbo is voorstellings van hoeke. Elke hoek bestaan uit twee bene en 'n hoekpunt. AB en BC is die bene van bostaande hoeke. Die grootte van 'n hoek is die hoeveelheid draaiing wat die een been weg van die ander om die hoekpunt gedraai het. </p> <div class="mw-heading mw-heading2"><h2 id="Grootte_van_'n_hoek:_Graad"><span id="Grootte_van_.27n_hoek:_Graad"></span>Grootte van 'n hoek: Graad</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Meetkundige_begrippe&veaction=edit&section=2" title="Wysig afdeling: Grootte van 'n hoek: Graad" class="mw-editsection-visualeditor"><span>wysig</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Meetkundige_begrippe&action=edit&section=2" title="Edit section's source code: Grootte van 'n hoek: Graad"><span>wysig bron</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Soos wat massa, inhoud, tyd, geld en lengte hulle eie eenhede het waarmee hulle groottes bepaal kan word, het 'n hoek ook 'n eenheid waarmee sy grootte bepaal word. Die eenheid is graad (mv. grade). </p><p>a. Ons begin by enige punt, sê punt A, op die sirkel en beweeg rondom die sirkel tot weer by A. Ons sê dat ons een <b>omwenteling</b> voltooi het, omdat ons een keer om die sirkel beweeg het. </p><p>b. In die tyd van die Babiloniërs het hulle sterrekundiges vasgestel dat dit die son 360 dae neem om by sy oorspronklike posisie in die hemelruim te kom. Daarom het hulle besluit om 'n sirkel in 360 gelyke dele te verdeel en elke deeltjie 'n graad te noem. Ons maak vandag nog van hierdie indeling gebruik. </p><p>c. <b>1 omwenteling = 360 grade.</b> </p><p>d. As ons nou ons sirkel presies in die helfte verdeel, kry ons twee halwe sirkels. </p><p>Ons sien nou dat daar 180 grade in 'n halwe sirkel of halwe omwenteling is. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Halwe_sirkel.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Halwe_sirkel.png/220px-Halwe_sirkel.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Halwe_sirkel.png/330px-Halwe_sirkel.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/ba/Halwe_sirkel.png/440px-Halwe_sirkel.png 2x" data-file-width="504" data-file-height="283" /></a><figcaption></figcaption></figure> <p>e. As ons nou die halwe sirkels weer in die helfte verdeel, kry ons vier kwartsirkels, of kwartomwentelings. </p><p>Ons sien nou dat daar 90 grade in 'n kwart sirkel of kwart omwenteling is. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Kwart_sirkel.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Kwart_sirkel.png/220px-Kwart_sirkel.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Kwart_sirkel.png/330px-Kwart_sirkel.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0a/Kwart_sirkel.png/440px-Kwart_sirkel.png 2x" data-file-width="531" data-file-height="299" /></a><figcaption></figcaption></figure> <p>f. As die sirkel in 360 gelyke dele verdeel word, sal elke deel 1 graad groot wees. </p><p>g. <b>Gevolgtrekking:</b> </p><p>1 omwenteling = 360 grade. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08a269880242c2132aae545154f2d4c3deb5d303" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.42ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{2}}\right)}"></span> omwenteling = 180 grade. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{4}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{4}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f83803ad2dab8892ea838849f2e1ceccccd0a6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.42ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{4}}\right)}"></span> omwenteling = 90 grade. </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{360}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>360</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{360}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14201f30d79a67cd10113f44859abd548c0730ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:7.745ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{360}}\right)}"></span> omwenteling = 1 graad </p><p>'n Hoek wat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{4}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{4}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f83803ad2dab8892ea838849f2e1ceccccd0a6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.42ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{4}}\right)}"></span> omwenteling groot is, noem ons 'n <b>regte hoek</b>. </p><p>regte hoek = 90 grade. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Kwart_omwenteling.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Kwart_omwenteling.png/220px-Kwart_omwenteling.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Kwart_omwenteling.png/330px-Kwart_omwenteling.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Kwart_omwenteling.png/440px-Kwart_omwenteling.png 2x" data-file-width="479" data-file-height="269" /></a><figcaption></figcaption></figure> <p>'n Hoek wat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {1}{2}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {1}{2}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08a269880242c2132aae545154f2d4c3deb5d303" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:5.42ex; height:6.176ex;" alt="{\displaystyle \left({\frac {1}{2}}\right)}"></span> omwenteling groot is, noem ons 'n <b>gestrekte hoek</b>. </p><p>gestrekte hoek = 180 grade. </p> <figure class="mw-default-size mw-halign-center" typeof="mw:File/Thumb"><a href="/wiki/L%C3%AAer:Halwe_omwenteling.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Halwe_omwenteling.png/220px-Halwe_omwenteling.png" decoding="async" width="220" height="124" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Halwe_omwenteling.png/330px-Halwe_omwenteling.png 1.5x, //upload.wikimedia.org/wikipedia/commons/1/10/Halwe_omwenteling.png 2x" data-file-width="437" data-file-height="246" /></a><figcaption></figcaption></figure> <p>'n Hoek wat kleiner as 'n regte hoek is, noem ons 'n <b>skerphoek</b>. </p><p>'n Hoek wat groter as 'n regte hoek maar kleiner as 'n gestrekte hoek is, noem ons 'n <b>stomphoek</b>. </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; 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