http://geometrie.idea-sketch.com/index.php?action=history&feed=atom&title=L%C3%B6sung_von_Aufgabe_9.4P_%28WS_12_13%29 Lösung von Aufgabe 9.4P (WS 12 13) - Versionsgeschichte 2026-08-14T12:44:35Z Versionsgeschichte dieser Seite in Geometrie-Wiki MediaWiki 1.43.9 http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_9.4P_(WS_12_13)&diff=20172&oldid=prev Tutorin Anne am 14. Januar 2013 um 12:10 Uhr 2013-01-14T12:10:30Z <p></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 14. Januar 2013, 12:10 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">Zeile 19:</td> <td colspan="2" class="diff-lineno">Zeile 19:</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>Fall 3 lässt sich analog zu Fall 2 beweisen. (Nicht extra nötig)--[[Benutzer:Tutorin Anne|Tutorin Anne]] 13:04, 14. Jan. 2013 (CET)&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>Fall 3 lässt sich analog zu Fall 2 beweisen. (Nicht extra nötig)--[[Benutzer:Tutorin Anne|Tutorin Anne]] 13:04, 14. Jan. 2013 (CET)&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 colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">&lt;ggb_applet width="585" height="422"  version="4.2" ggbBase64="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" showResetIcon = "false" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "true" showToolBar = "true" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</ins></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;"><div>Fall 2: &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>Fall 2: &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;"><div>{| class=&quot;wikitable&quot;  </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>{| class=&quot;wikitable&quot;  </div></td></tr> <!-- diff cache key geometrie:diff:1.41:old-20171:rev-20172:php=table --> </table> Tutorin Anne http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_9.4P_(WS_12_13)&diff=20171&oldid=prev Tutorin Anne am 14. Januar 2013 um 12:04 Uhr 2013-01-14T12:04:14Z <p></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 14. Januar 2013, 12:04 Uhr</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Zeile 1:</td> <td colspan="2" class="diff-lineno">Zeile 1:</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>&#039;&#039;m&#039;&#039; sei Mittelsenkrechte der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;. Beweisen Sie durch Kontraposition: &lt;math&gt;\left| AP \right| =\left| BP \right|\Rightarrow  P\in m&lt;/math&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>&#039;&#039;m&#039;&#039; sei Mittelsenkrechte der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;. Beweisen Sie durch Kontraposition: &lt;math&gt;\left| AP \right| =\left| BP \right|\Rightarrow  P\in m&lt;/math&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;"><div>&lt;br /&gt;Tipp: Nutzen Sie den Satz von Pasch und die Dreiecksungleichung. &lt;br /&gt;Hinweis: Die Umkehrung des hier zu beweisenden Satzes sei bereits bewiesen.&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>&lt;br /&gt;Tipp: Nutzen Sie den Satz von Pasch und die Dreiecksungleichung. &lt;br /&gt;Hinweis: Die Umkehrung des hier zu beweisenden Satzes sei bereits bewiesen.&lt;br /&gt;</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">In der Vorlesung hat Herr Schnirch schon den Tipp gegeben, den Beweis indirekt zu führen. Ob man nun die Kontraposition oder einen Widerspruchsbeweis wählt, ist egal. (Es handelt sich um die selben Schritte.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Ich mache hier mal den Anfang.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{| class="wikitable" </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| Voraussetzung || ''m'' sei Mittelsenkrechte der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;. &lt;math&gt;\left| AP \right| =\left| BP \right|&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| Behauptung || &lt;math&gt;P\in m&lt;/math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| Annahme || &lt;math&gt;P \not\in m &lt;/math&gt; </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Fallunterscheidung je nach Lage von P.&lt;br /&gt; Nach der Annahme liegt P entweder auf AB (Fall 1), oder in der Halbebenen gA^+ (ohne auf AB zu liegen)(Fall 2) oder in gA- (Fall 3). &lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Fall 1 kann nicht eintreten, da P nach Voraussetzung ja Mittelpunkt der STrecke AB wäre und damit auf m liegen würde.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Fall 2 genauer zu betrachen und zum Widerspruch zu führen.&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Fall 3 lässt sich analog zu Fall 2 beweisen. (Nicht extra nötig)--[[Benutzer:Tutorin Anne|Tutorin Anne]] 13:04, 14. Jan. 2013 (CET)&lt;br /&gt;&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">Fall 2: &lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">{| class="wikitable" </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">!Beweisschritt!!Begründung</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| 1 (Schritt 1 hier)|| (Begründung 1)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| 2 (Schritt 2) || (Begründung 2)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| 3 (Schritt) || (Begründung)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|- </ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">| 4 (Schritt) || (Begründung und weitere Schritte ergänzen)</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">|}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;">&lt;br /&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></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><ins style="font-weight: bold; text-decoration: none;"></ins></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>[[Kategorie:Einführung_P]]</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>[[Kategorie:Einführung_P]]</div></td></tr> </table> Tutorin Anne http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_9.4P_(WS_12_13)&diff=20041&oldid=prev Schnirch: Die Seite wurde neu angelegt: „''m'' sei Mittelsenkrechte der Strecke <math>\overline{AB}</math>. Beweisen Sie durch Kontraposition: <math>\left| AP \right| =\left| BP \right|\Rightarrow P\in …“ 2013-01-08T13:10:46Z <p>Die Seite wurde neu angelegt: „&#039;&#039;m&#039;&#039; sei Mittelsenkrechte der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;. Beweisen Sie durch Kontraposition: &lt;math&gt;\left| AP \right| =\left| BP \right|\Rightarrow P\in …“</p> <p><b>Neue Seite</b></p><div>&#039;&#039;m&#039;&#039; sei Mittelsenkrechte der Strecke &lt;math&gt;\overline{AB}&lt;/math&gt;. Beweisen Sie durch Kontraposition: &lt;math&gt;\left| AP \right| =\left| BP \right|\Rightarrow P\in m&lt;/math&gt;<br /> &lt;br /&gt;Tipp: Nutzen Sie den Satz von Pasch und die Dreiecksungleichung. &lt;br /&gt;Hinweis: Die Umkehrung des hier zu beweisenden Satzes sei bereits bewiesen.&lt;br /&gt;<br /> <br /> [[Kategorie:Einführung_P]]</div> Schnirch