http://geometrie.idea-sketch.com/index.php?action=history&feed=atom&title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13 Basiswinkelsatz und Mittelsenkrechtenkriterium SoSe 13 - Versionsgeschichte 2026-08-14T11:30:27Z Versionsgeschichte dieser Seite in Geometrie-Wiki MediaWiki 1.43.9 http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24087&oldid=prev *m.g.*: /* Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes */ 2013-06-30T06:37:58Z <p><span class="autocomment">Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:37 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l23">Zeile 23:</td> <td colspan="2" class="diff-lineno">Zeile 23:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten. --[[Benutzer:*m.g.*|*m.g.*]] 08:34, 30. Jun. 2013 (CEST)&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten. --[[Benutzer:*m.g.*|*m.g.*]] 08:34, 30. Jun. 2013 (CEST)&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}} </del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24086:rev-24087:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24086&oldid=prev *m.g.*: /* Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes */ 2013-06-30T06:34:39Z <p><span class="autocomment">Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:34 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l21">Zeile 21:</td> <td colspan="2" class="diff-lineno">Zeile 21:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Letztlich hilft nur die Winkelhalbierende des Winkels, der der Basis des gleichschenkligen Dreiecks gegenüberliegt. Die Winkelhalbierende muss dann die Basis des Dreiecks schneiden. Diese unmittelbar einsichtige Tatsache muss eigentlich bwiesen werden. Wir verweisen diesbezüglich auf die [[Lemmata zu Winkeln]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Letztlich hilft nur die Winkelhalbierende des Winkels, der der Basis des gleichschenkligen Dreiecks gegenüberliegt. Die Winkelhalbierende muss dann die Basis des Dreiecks schneiden. Diese unmittelbar einsichtige Tatsache muss eigentlich bwiesen werden. Wir verweisen diesbezüglich auf die [[Lemmata zu Winkeln]].</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten.--[[Benutzer:*m.g.*|*m.g.*]] <del style="font-weight: bold; text-decoration: none;">18</del>:<del style="font-weight: bold; text-decoration: none;">17</del>, <del style="font-weight: bold; text-decoration: none;">21</del>. Jun. <del style="font-weight: bold; text-decoration: none;">2012 </del>(CEST)<del style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</del>&lt;br /&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten. --[[Benutzer:*m.g.*|*m.g.*]] <ins style="font-weight: bold; text-decoration: none;">08</ins>:<ins style="font-weight: bold; text-decoration: none;">34</ins>, <ins style="font-weight: bold; text-decoration: none;">30</ins>. Jun. <ins style="font-weight: bold; text-decoration: none;">2013 </ins>(CEST)&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}}  </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}}  </div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24085:rev-24086:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24085&oldid=prev *m.g.*: /* Beweis mittels Euklidischer Geometrie */ 2013-06-30T06:33:07Z <p><span class="autocomment">Beweis mittels Euklidischer Geometrie</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:33 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l98">Zeile 98:</td> <td colspan="2" class="diff-lineno">Zeile 98:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Wenn ein Dreieck zwei zueinander kongruente Innenwinkel hat, dann ist das Dreieck gleichschenklig.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>::Wenn ein Dreieck zwei zueinander kongruente Innenwinkel hat, dann ist das Dreieck gleichschenklig.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">======Beweis mittels Euklidischer Geometrie======</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{#ev:youtube|yASKusZIfOo&amp;sns}}</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Ist an dieser Stelle leider noch nicht erlaubt. Man könnte sonst aber so beweisen.--[[Benutzer:*m.g.*|*m.g.*]] 22:04, 21. Jan. 2013 (CET)</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24084:rev-24085:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24084&oldid=prev *m.g.*: /* Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes */ 2013-06-30T06:32:41Z <p><span class="autocomment">Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:32 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l23">Zeile 23:</td> <td colspan="2" class="diff-lineno">Zeile 23:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten.--[[Benutzer:*m.g.*|*m.g.*]] 18:17, 21. Jun. 2012 (CEST)&lt;br /&gt;&lt;br /&gt;</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten.--[[Benutzer:*m.g.*|*m.g.*]] 18:17, 21. Jun. 2012 (CEST)&lt;br /&gt;&lt;br /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}} <del style="font-weight: bold; text-decoration: none;">finden Sie das Arbeitsblatt zum Beweis des Basiswinkelsatzes aus der Vorlesung vom 28.06.2012.</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}}  </div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24083:rev-24084:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24083&oldid=prev *m.g.*: /* Beweis des Basiswinkelsatzes */ 2013-06-30T06:30:53Z <p><span class="autocomment">Beweis des Basiswinkelsatzes</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:30 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">Zeile 26:</td> <td colspan="2" class="diff-lineno">Zeile 26:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width="<del style="font-weight: bold; text-decoration: none;">636</del>" height="<del style="font-weight: bold; text-decoration: none;">415</del>"  version="3.2" 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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "true" showAlgebraInput = "false" allowRescaling = "true" /&gt;</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width="<ins style="font-weight: bold; text-decoration: none;">1000</ins>" height="<ins style="font-weight: bold; text-decoration: none;">800</ins>"  version="3.2" 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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "true" showAlgebraInput = "false" allowRescaling = "true" /&gt;</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Das Mittelsenkrechtenkriterium ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Das Mittelsenkrechtenkriterium ==</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24082:rev-24083:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24082&oldid=prev *m.g.*: /* Beweis des Basiswinkelsatzes */ 2013-06-30T06:30:03Z <p><span class="autocomment">Beweis des Basiswinkelsatzes</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="de"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Nächstältere Version</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Version vom 30. Juni 2013, 06:30 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">Zeile 26:</td> <td colspan="2" class="diff-lineno">Zeile 26:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>====== Beweis des Basiswinkelsatzes ======</div></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;ggb_applet width="<del style="font-weight: bold; text-decoration: none;">1272</del>" height="<del style="font-weight: bold; text-decoration: none;">830</del>"  version="3.2" 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" 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border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Das Mittelsenkrechtenkriterium ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Das Mittelsenkrechtenkriterium ==</div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-24080:rev-24082:php=table --> </table> *m.g.* http://geometrie.idea-sketch.com/index.php?title=Basiswinkelsatz_und_Mittelsenkrechtenkriterium_SoSe_13&diff=24080&oldid=prev *m.g.*: Die Seite wurde neu angelegt: „<div style="margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#FFFF99; align:left;"> {|width=90%| style="background…“ 2013-06-30T06:27:19Z <p>Die Seite wurde neu angelegt: „&lt;div style=&quot;margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#FFFF99; align:left;&quot;&gt; {|width=90%| style=&quot;background…“</p> <p><b>Neue Seite</b></p><div>&lt;div style=&quot;margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#FFFF99; align:left;&quot;&gt;<br /> {|width=90%| style=&quot;background-color:#FFFF99; padding:1em&quot;<br /> | valign=&quot;top&quot; |<br /> <br /> <br /> <br /> == Der Basiswinkelsatz ==<br /> === Gleichschenklige Dreiecke ===<br /> ===== Definition VII.4 : (gleichschenkliges Dreieck) =====<br /> Das können sie selbst. Bringen Sie in der Definition die Begriffe Basis, Basiswinkel und Schenkel eines gleichschenkligen Dreiecks unter.<br /> <br /> Übungsaufgabe<br /> <br /> === Der Basiswinkelsatz ===<br /> ===== Satz VII.5: Basiswinkelsatz =====<br /> ::In jedem gleichschenkligen Dreieck sind die Basiswinkel kongruent zueinander.<br /> [[Schulvariante des Beweises des Basiswinkelsatzes]]<br /> <br /> ===== Ein im Rahmen unserer Theorie korrekter Beweis des Basiswinkelsatzes =====<br /> Probieren Sie ruhig weitere Varianten: Mittelsenkrechte ... .<br /> Letztlich hilft nur die Winkelhalbierende des Winkels, der der Basis des gleichschenkligen Dreiecks gegenüberliegt. Die Winkelhalbierende muss dann die Basis des Dreiecks schneiden. Diese unmittelbar einsichtige Tatsache muss eigentlich bwiesen werden. Wir verweisen diesbezüglich auf die [[Lemmata zu Winkeln]].<br /> <br /> Hinweis: Im folgenden Beweis berufen wir uns auf Lemma 1. Korrekterweise müsste es Lemma W/3 heißen. Sobald ich Zeit finde werde ich die App überarbeiten.--[[Benutzer:*m.g.*|*m.g.*]] 18:17, 21. Jun. 2012 (CEST)&lt;br /&gt;&lt;br /&gt;<br /> <br /> {{pdf|Beweis_des_Basiswinkelsatzes.pdf| Hier}} finden Sie das Arbeitsblatt zum Beweis des Basiswinkelsatzes aus der Vorlesung vom 28.06.2012.<br /> <br /> ====== Beweis des Basiswinkelsatzes ======<br /> &lt;ggb_applet width=&quot;1272&quot; height=&quot;830&quot; version=&quot;3.2&quot; 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&quot; framePossible = &quot;false&quot; showResetIcon = &quot;true&quot; showAnimationButton = &quot;true&quot; enableRightClick = &quot;true&quot; errorDialogsActive = &quot;true&quot; enableLabelDrags = &quot;true&quot; showMenuBar = &quot;false&quot; showToolBar = &quot;false&quot; showToolBarHelp = &quot;true&quot; showAlgebraInput = &quot;false&quot; allowRescaling = &quot;true&quot; /&gt;<br /> <br /> == Das Mittelsenkrechtenkriterium ==<br /> ===== Satz VII.6: (Mittelsenkrechtenkriterium) =====<br /> ::::Ein Punkt &lt;math&gt;\ P&lt;/math&gt; gehört genau dann zur Mittelsenkrechten der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;, wenn &lt;math&gt;\overline{AP} \tilde {=} \overline{BP}&lt;/math&gt; gilt.<br /> <br /> &lt;br&gt;<br /> <br /> <br /> =====Bezug zur Schule:=====<br /> Konstruktion der Mittelsenkrechten einer Strecke &lt;math&gt;\overline{AB}&lt;/math&gt; mittels Zirkel und Lineal:<br /> <br /> &lt;u&gt;Konstruktionsvorschrift:&lt;/u&gt;<br /> <br /> &lt;u&gt;gegeben:&lt;/u&gt; Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;<br /> <br /> &lt;u&gt;gesucht:&lt;/u&gt; &lt;math&gt;\ m&lt;/math&gt; , die Mittelsenkrechte von &lt;math&gt;\overline{AB}&lt;/math&gt;<br /> <br /> <br /> {| class=&quot;wikitable center&quot;<br /> |- style=&quot;background: #DDFFDD;&quot;<br /> ! Schrittnr.<br /> ! Konstruktionsschritt<br /> |-<br /> | 1.<br /> | Zeichne einen Kreis um &lt;math&gt;\ A&lt;/math&gt;, dessen Radius &lt;math&gt;\ r&lt;/math&gt; länger als die Hälfte der Länge der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt; ist.<br /> |-<br /> | 2.<br /> | Behalte &lt;math&gt;\ r&lt;/math&gt; bei und zeichne einen Kreis um &lt;math&gt;\ B&lt;/math&gt;.<br /> |-<br /> | 3.<br /> | Der Kreis um &lt;math&gt;\ A&lt;/math&gt; schneidet den Kreis um &lt;math&gt;\ B&lt;/math&gt; in den beiden Schnittpunkten &lt;math&gt;\ S_1&lt;/math&gt; und &lt;math&gt;\ S_2&lt;/math&gt;.<br /> |-<br /> | 4.<br /> | Zeichne die Gerade &lt;math&gt;\ S_1S_2&lt;/math&gt;. Sie ist die gesuchte Mittelsenkrechte von &lt;math&gt;\overline{AB}&lt;/math&gt;.<br /> |}<br /> <br /> &lt;u&gt;Frage:&lt;/u&gt; &#039;&#039;Ist dieser Algorithmus korrekt?&#039;&#039; Anders gefragt: Ist &lt;math&gt;\ S_1S_2&lt;/math&gt; wirklich die Mittelsenkrechte von &lt;math&gt;\overline{AB}&lt;/math&gt;?<br /> <br /> Wir beweisen die Korrektheit der Konstruktion indem wir folgendes zeigen:<br /> <br /> ===== Satz VII.6 a: =====<br /> ::Wenn ein Punkt &lt;math&gt;\ P&lt;/math&gt; zu den Endpunkten der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt; jeweils ein und denselben Abstand hat, so ist er ein Punkt der Mittelsenkrechten von &lt;math&gt;\overline{AB}&lt;/math&gt;.<br /> <br /> ===== Beweis von Satz VII.6 a =====<br /> <br /> Übungsaufgabe (Das Video hilft)<br /> <br /> {{#ev:youtube|SV7e7lTCPps}}<br /> <br /> <br /> Nach dem Beweis von Satz VII.6 a wissen wir, dass die beiden Punkte &lt;math&gt;\ S_1&lt;/math&gt; und &lt;math&gt;\ S_2&lt;/math&gt; Punkte der Mittelsenkrechten von &lt;math&gt;\overline{AB}&lt;/math&gt; sind.<br /> <br /> Die Wahl des Radius &lt;math&gt;\ r&lt;/math&gt; der beiden Kreise in unserer Konstruktion war beliebig für &lt;math&gt;\ | r | &gt; \frac{1}{2} | \overline{AB} |&lt;/math&gt;. Wir stellen uns jetzt die frage, ob wir jeden beliebigen Punkt unserer Mittelsenkrechten als Schnittpunkt zweier entsprechender Kreise konstruieren könnten.<br /> <br /> Die Frage anders formuliert:<br /> <br /> Hat jeder Punkt der Mittelsenkrechten von &lt;math&gt;\overline{AB}&lt;/math&gt; zu den Punkten &lt;math&gt;\ A&lt;/math&gt; und &lt;math&gt;\ B&lt;/math&gt; jeweils ein und denselben Abstand?<br /> <br /> Noch anders formuliert:<br /> <br /> Hat jeder Punkt der Mittelsenkrechten einer Strecke &lt;math&gt;\overline{AB}&lt;/math&gt; notwendigerweise zu &lt;math&gt;\ A&lt;/math&gt; und zu &lt;math&gt;\ B&lt;/math&gt; ein und denselben Abstand?<br /> <br /> Der folgende Satz VII.6 b beantwortet diese beiden Fragen postiv:<br /> <br /> ===== Satz VII.6 b =====<br /> ::Wenn ein Punkt &lt;math&gt;\ P&lt;/math&gt; zur Mittelsenkrechten der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt; gehört, dann hat er zu den Punkten &lt;math&gt;\ A&lt;/math&gt; und &lt;math&gt;\ B&lt;/math&gt; ein und denselben Abstand.<br /> Beweis: Übungsaufgabe<br /> ==Die Umkehrung des Basiswinkelsatzes==<br /> ===== Satz VII.7=====<br /> ::Wenn ein Dreieck zwei zueinander kongruente Innenwinkel hat, dann ist das Dreieck gleichschenklig.<br /> <br /> ======Beweis mittels Euklidischer Geometrie======<br /> {{#ev:youtube|yASKusZIfOo&amp;sns}}<br /> <br /> Ist an dieser Stelle leider noch nicht erlaubt. Man könnte sonst aber so beweisen.--[[Benutzer:*m.g.*|*m.g.*]] 22:04, 21. Jan. 2013 (CET)<br /> <br /> <br /> <br /> &lt;!--- Was hier drunter steht muss stehen bleiben ---&gt;<br /> |}<br /> &lt;/div&gt;<br /> <br /> [[Kategorie:Einführung_S]]</div> *m.g.*