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勾股定理逆定理的5种方法 （那个错了）勾股定理逆定理的五种应用 “如果一个三角形的三条边长分别为a、b、c，且有  ，那么这个三角形是直角三角形。”这就是勾股定理的逆定理。它是初中几何中极其重要的一个定理，有着广泛的应用。下面举例说明。一. 用于判断三角形的形状 例1. 如图1， 中，，，，求证：是直角三角形证明：由已知得： ，即c是最长边是直角三角形二. 用于求角度 例2. 如图2，点P是等边 内一点，且，，，求的度数解：因 ，以点B为定点，将旋转到达的位置，连结PP”，则为等边三角形在 中由勾股定理的逆定理知三. 用于求边长 例3. 如图3，在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image002.gif[/img]中，D是BC边上的点，已知[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image029.gif[/img]，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image030.gif[/img]，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image031.gif[/img]，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image032.gif[/img]，求DC的长。 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image033.gif[/img] 解：在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image034.gif[/img]中，由[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image035.gif[/img]可知[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image036.gif[/img] 又由勾股定理的逆定理知 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image037.gif[/img] 在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image038.gif[/img]中 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image039.gif[/img] 四. 用于求面积 例4. 如图4，已知[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image040.gif[/img]，AB＝3，BC＝4，CD＝12，DA＝13。求四边形ABCD的面积。 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image041.gif[/img] 解：连结AC，在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image042.gif[/img]中，由勾股定理得[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image043.gif[/img] 在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image044.gif[/img]中 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image045.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image026.gif[/img]由勾股定理的逆定理知 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image046.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image047.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image048.gif[/img] 五. 用于证明垂直 例5. 如图5，已知正方形ABCD中，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image049.gif[/img]，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image050.gif[/img]，求证：[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image051.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image052.gif[/img] 证明：连结FC，设AF＝1，则DF＝3，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image053.gif[/img]，[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image054.gif[/img] 在[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image055.gif[/img]、[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image056.gif[/img]、[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image057.gif[/img]中 [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image058.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image059.gif[/img] [img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image026.gif[/img]由勾股定理的逆定理知[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image060.gif[/img] 即[img]http://res.tongyi.com/resources/old_article/educa/unvisity/zxxzt/e9/ztfd/39.files/image051.gif[/img] |
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沙发#
发布于：2018-01-26 21:29
发不出来哎
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板凳#
发布于：2018-01-26 21:29
无语了。。。
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地板#
发布于：2018-01-27 10:43
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4楼#
发布于：2018-01-27 18:24
666
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5楼#
发布于：2018-01-27 18:27
wlm5421926：无语了。。。回到原帖，，，从三开始，后面一片是什么东西 |
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