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	<id>http://geometrie.idea-sketch.com/index.php?action=history&amp;feed=atom&amp;title=L%C3%B6sung_von_Aufgabe_12.08_SoSe_13</id>
	<title>Lösung von Aufgabe 12.08 SoSe 13 - Versionsgeschichte</title>
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	<updated>2026-08-11T00:25:06Z</updated>
	<subtitle>Versionsgeschichte dieser Seite in Geometrie-Wiki</subtitle>
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		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_12.08_SoSe_13&amp;diff=24927&amp;oldid=prev</id>
		<title>*m.g.* am 18. Juli 2013 um 21:01 Uhr</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_12.08_SoSe_13&amp;diff=24927&amp;oldid=prev"/>
		<updated>2013-07-18T21:01:56Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw=&quot;interface&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
				&lt;tr class=&quot;diff-title&quot; lang=&quot;de&quot;&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Nächstältere Version&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Version vom 18. Juli 2013, 21:01 Uhr&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Zeile 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Zeile 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;| valign=&amp;quot;top&amp;quot; |&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;| valign=&amp;quot;top&amp;quot; |&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;==Aufgabe 12.08 ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Beweisen Sie: Die Höhen eines Dreiecks schneiden sich in genau einem Punkt. Das folgende Applet hilft:&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ggb_applet width=&quot;755&quot; height=&quot;502&quot;  version=&quot;3.2&quot; ggbBase64=&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; /&amp;gt;&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Hinweis: Ein Klick auf den Button Rechts unten liefert die Konstruktionsbeschreibung.&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;==Lösung==&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;==Lösung==&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;Die Mittelsenkrechten von &amp;lt;math&amp;gt;\overline{A&#039;B&#039;C&#039;}&amp;lt;/math&amp;gt; sind die Geraden, auf denen die Höhen von &amp;lt;math&amp;gt;\overline{ABC}&amp;lt;/math&amp;gt; liegen.--[[Benutzer:*m.g.*|*m.g.*]] 23:01, 18. Jul. 2013 (CEST)&amp;lt;br /&amp;gt;&amp;lt;br /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt; &lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;Zurück zu: [[Serie 12 SoSe 2013]]&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;Zurück zu: [[Serie 12 SoSe 2013]]&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;!--- Was hier drunter steht muss stehen bleiben ---&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;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;&quot;&gt;&lt;div&gt;&amp;lt;!--- Was hier drunter steht muss stehen bleiben ---&amp;gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;

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&lt;/table&gt;</summary>
		<author><name>*m.g.*</name></author>
	</entry>
	<entry>
		<id>http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_12.08_SoSe_13&amp;diff=24885&amp;oldid=prev</id>
		<title>*m.g.*: 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…“</title>
		<link rel="alternate" type="text/html" href="http://geometrie.idea-sketch.com/index.php?title=L%C3%B6sung_von_Aufgabe_12.08_SoSe_13&amp;diff=24885&amp;oldid=prev"/>
		<updated>2013-07-18T19:50:28Z</updated>

		<summary type="html">&lt;p&gt;Die Seite wurde neu angelegt: „&amp;lt;div style=&amp;quot;margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#FFFF99; align:left;&amp;quot;&amp;gt; {|width=90%| style=&amp;quot;background…“&lt;/p&gt;
&lt;p&gt;&lt;b&gt;Neue Seite&lt;/b&gt;&lt;/p&gt;&lt;div&gt;&amp;lt;div style=&amp;quot;margin:0; margin-right:4px; border:1px solid #27408B; padding: 1em 1em 1em 1em; background-color:#FFFF99; align:left;&amp;quot;&amp;gt;&lt;br /&gt;
{|width=90%| style=&amp;quot;background-color:#FFFF99; padding:1em&amp;quot;&lt;br /&gt;
| valign=&amp;quot;top&amp;quot; |&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
==Lösung==&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Zurück zu: [[Serie 12 SoSe 2013]]&lt;br /&gt;
&amp;lt;!--- Was hier drunter steht muss stehen bleiben ---&amp;gt;&lt;br /&gt;
|}&lt;br /&gt;
&amp;lt;/div&amp;gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
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[[Kategorie:Einführung_S]]&lt;/div&gt;</summary>
		<author><name>*m.g.*</name></author>
	</entry>
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