https://peda.net/id/88c00e0e449 2019-03-12T10:05:00+02:00 https://peda.net/:static/537/peda.net.logo.bg.svg <div class="license">Tämän sivun lisenssi <a rel="license" href="https://peda.net/info">Peda.net-yleislisenssi</a></div> https://peda.net/id/e59e819e6a9 2024-02-29T11:16:36+02:00 Open Geogebra Geometry either as a desktop app, as a mobile app, or as a browser version. For ease of access, you may use the following link:<br/> <br/> <a href="https://www.geogebra.org/geometry" rel="nofollow ugc noopener">https://www.geogebra.org/geometry</a><br/> <br/> <ol> <li><b>Triangle angle sum theorem</b> <ul> <li>Use the point and line segment tools to draw a triangle of any kind.</li> <li>Name the vertices A, B, and C if they do not have these names automatically.</li> <li>Use the parallel line tool to draw a line that is parallel to the side AB through vertex C.</li> <li>Use the angle tool to mark the angles BAC (angle at vertex A), CBA (angle at vertex B), and ACB (angle at vertex C). Name the angles <span>α</span>, <span>β</span>, and <span>γ, in the preceding order for A, B, and C.</span></li> <li>Use the angle tool to mark the other angles at vertex A: one of them should be of identical size to β with AC as one of its sides, and one of them should be of identical size to α with BC as one of its sides.<br/> <ul> <li><span>Hint: You may have to add points to the parallel line using the point tool.</span></li> </ul> </li> <li><span>Add a text field using the text tool. Under additional settings, you will find a menu with the geogebra logo on it.</span> <ul> <li><span>Choose α from this list.</span></li> <li><span>Type the following symbol: +</span></li> <li><span>Choose β from this list.</span></li> <li><span>Type the following symbol: +</span></li> <li><span>Choose γ from this list.</span></li> </ul> </li> <li><span><em>What did you accomplish and why?</em></span></li> </ul> </li> <li><b><span>Reflections with respect to a line</span></b> <ul> <li>Right click on the white plane canvas. <ul> <li>Under coordinate grid options, select the largest squares.</li> </ul> </li> <li><span>Use the line tool to draw a line in any direction.</span></li> <li><span>Use the polygon tool to draw a polygon of any kind.</span></li> <li><span>Use the reflection tool to create a mirror image of the polygon with respect to the line.</span></li> <li>Use the arrow tool to move your polygon.<br/> <ul> <li><span><em>If you move the polygon to the left, where does its mirror image move?</em></span></li> <li><span><em>If you move the polygon two steps to the right and five steps upwards (you might remember this from Khan Academy as [[$(x+2,y+5)$]]), how many steps and in which direction does its mirror image move?</em></span></li> </ul> </li> </ul> </li> <li><b><span>Reflections with respect to a point</span></b> <ul> <li>Right click on the white plane canvas.</li> <li>Under coordinate grid options, select the largest squares.</li> <li><span>Use the point tool to draw a point.</span></li> <li><span>Use the polygon tool to draw a polygon of any kind.</span></li> <li><span>Use the reflection tool to create a mirror image of the polygon with respect to the point.</span></li> <li>Use the arrow tool to move your polygon.<br/> <ul> <li><span><em>If you move the polygon to the left, where does its mirror image move?</em></span></li> <li><span><em>If you move the polygon two steps to the right and five steps upwards (you might remember this from Khan Academy as [[$(x+2,y+5)$]]), how many steps and in which direction does its mirror image move?</em></span></li> </ul> </li> </ul> </li> <li><b><span>Challenging task</span></b> <ul> <li><span><em>Solve the challenging task using geogebra.</em><a href="https://peda.net/p/janne.rytkonen/ym/2-tasogeometria/kertaus/9#top" title="9B0E2BF3-7112-41D5-8019-CD6A45F9F041.jpeg"><img src="https://peda.net/p/janne.rytkonen/ym/2-tasogeometria/kertaus/9:file/photo/eb83f5f28731c85b4740fc72c254a1d2e3f106db/9B0E2BF3-7112-41D5-8019-CD6A45F9F041.jpeg" alt="" title="Challenging task" class="inline" loading="lazy"/></a></span></li> <li><span>Remember to refer to chapter <a href="https://peda.net/p/janne.rytkonen/ym/2-tasogeometria/kmp#top" class="uuid-2e829b86-23fd-11e7-852f-eaecf9f45fbc">2.12 Kolmion merkilliset pisteet</a>​ for details on how to draw a circle within a triangle.</span></li> </ul> </li> </ol> 2020-03-20T12:38:11+02:00