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2022年勾股定理知识点总结2 .pdf

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1、_ 精品资料勾股定理全章知识点归纳总结一基础知识点：1：勾股定理直角三角形两直角边a、b 的平方和等于斜边c 的平方。（即：a2+b2c2）要点诠释：勾股定理反映了直角三角形三边之间的关系，是直角三角形的重要性质之一，其主要应用：（1）已知直角三角形的两边求第三边（在ABC中，90C，则22cab，22bca，22acb）（2）已知直角三角形的一边与另两边的关系，求直角三角形的另两边（3）利用勾股定理可以证明线段平方关系的问题2：勾股定理的逆定理如果三角形的三边长：a、b、c，则有关系 a2+b2c2，那么这个三角形是直角三角形。要点诠释：勾股定理的逆定理是判定一个三角形是否是直角三角形的一种

2、重要方法，它通过“数转化为形”来确定三角形的可能形状，在运用这一定理时应注意：（1）首先确定最大边，不妨设最长边长为：c；_ 精品资料（2）验证 c2与 a2+b2是否具有相等关系，若c2a2+b2，则ABC 是以 C 为直角的直角三角形（若 c2a2+b2，则 ABC 是以 C 为钝角的钝角三角形；若c2a2+b2，则 ABC 为锐角三角形）。（定理中a，b，c及222abc只是一种表现形式，不可认为是唯一的，如若三角形三边长a，b，c满足222acb，那么以a，b，c为三边的三角形是直角三角形，但是 b 为斜边）3：勾股定理与勾股定理逆定理的区别与联系区别：勾股定理是直角三角形的性质定理，

3、而其逆定理是判定定理；联系：勾股定理与其逆定理的题设和结论正好相反，都与直角三角形有关。4：互逆命题的概念如果一个命题的题设和结论分别是另一个命题的结论和题设，这样的两个命题叫做互逆命题。如果把其中一个叫做原命题，那么另一个叫做它的逆命题。规律方法指导1勾股定理的证明实际采用的是图形面积与代数恒等式的关系相互转化证明的。2勾股定理反映的是直角三角形的三边的数量关系，可以用于解决求解直角三角形边边关系的题目。3勾股定理在应用时一定要注意弄清谁是斜边谁直角边，这是这个知识在应用过程中易犯的主要错误。文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6

4、R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 Z

5、I1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6

6、R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 Z

7、I1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6

8、R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 Z

9、I1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6

10、R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料4.勾股定理的逆定理：如果三角形的三条边长a，b，c 有下列关系：a2+b2c2，?那么这个三角形是直角三角形；该逆定理给出判定一个三角形是否是直角三角形的判定方法5.?应用勾股定理的逆定理判定一个三角形是不是直角三角形的过程主要是进行代数运算，通过学习加深对“数形结合”的理解我们把题设、结论正好相反的两个命题叫做互逆命题。如果把其中一个叫做原命题，那么另一个叫做它的逆命题。（例：勾股定理与勾股定理逆定理）5：勾股定理的证明勾股定理的证明方法很

11、多，常见的是拼图的方法用拼图的方法验证勾股定理的思路是图形进过割补拼接后，只要没有重叠，没有空隙，面积不会改变根据同一种图形的面积不同的表示方法，列出等式，推导出勾股定理常见方法如下：方法一：4EFGHSSS正方形正方形 ABCD，2214()2abbac，化简可证方法二：cbaHGFEDCBAcbaHGFEDCBA文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE

12、4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J

13、6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE

14、4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J

15、6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE

16、4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J

17、6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料四个直角三角形的面积与小正

18、方形面积的和等于大正方形的面积四个直角三角形的面积与小正方形面积的和为221422Sabcabc大正方形面积为222()2Sabaabb所以222abc方法三：1()()2Sabab梯形，2112S222ADEABESSabc梯形，化简得证6：勾股数能够构成直角三角形的三边长的三个正整数称为勾股数，即222abc中，a，b，c为正整数时，称a，b，c为一组勾股数记住常见的勾股数可以提高解题速度，如3,4,5；6,8,10；5,12,13；7,24,25等用含字母的代数式表示n组勾股数：221,2,1nn n（2,nn为正整数）；2221,22,221nnnnn（n为正整数）2222,2,

19、mnmn mn（,mnm，n为正整数）二、经典例题精讲题型一：直接考查勾股定理例.在ABC中，90C已知6AC，8BC求 AB 的长abccbaEDCBAbacbaccabcabCBDA文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY

20、3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V

21、9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY

22、3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V

23、9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY

24、3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V

25、9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料已知17AB，15AC，求BC的长分析：直接应用勾股定理222abc解：2210ABACBC228BCABAC题型二：利用勾股定理测量长度例题 1 如果梯子的底端

26、离建筑物9 米，那么 15 米长的梯子可以到达建筑物的高度是多少米？解析：这是一道大家熟知的典型的“知二求一”的题。把实物模型转化为数学模型后，.已知斜边长和一条直角边长，求另外一条直角边的长度，可以直接利用勾股定理！根据勾股定理AC2+BC2=AB2,即 AC2+92=152,所以 AC2=144,所以 AC=12.例题 2如图（8），水池中离岸边D 点 1.5 米的 C 处，直立长着一根芦苇，出水部分 BC 的长是 0.5 米，把芦苇拉到岸边，它的顶端 B 恰好落到 D 点，并求水池的深度AC.文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3

27、V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9

28、 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3

29、V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9

30、 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3

31、V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9

32、 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3

33、V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料解析：同例题 1 一样，先将实物模型转化为数学模型，如图2.由题意可知ACD中,ACD=90 ,在 Rt ACD 中，只知道 CD=1.5，这是典型的利用勾股定理“知二求一”的类型。标准解题步骤如下（仅供参考）：解：如图 2，根据勾股定理，AC2+CD2=AD2设水深 AC=x 米，那么 AD=AB=AC+CB=x+0.5 x2+1.52=（x+0.5）2 解之得 x=2.故水深为2 米.题型三：勾股定理和逆定理并用例题 3 如图 3，正方

34、形 ABCD 中，E 是 BC 边上的中点，F 是 AB 上一点，且ABFB41那么DEF 是直角三角形吗？为什么？解析：这道题把很多条件都隐藏了，乍一看有点摸不着头脑。仔细读题会意可以发现规律，没有任何条件，我们也可以开创条件，由ABFB41可以设 AB=4a，那么 BE=CE=2 a,AF=3 a,BF=a,那么在 Rt AFD、Rt BEF 和 Rt CDE 中，分别利用勾股定理求出DF,EF 和 DE 的长，反过来再利用勾股定理逆定理去判断DEF 是否是直角三角形。详细解题步骤如下：文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

35、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

36、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

37、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

38、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

39、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

40、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

41、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料解：设正方形 ABCD 的边长为 4a,则 BE=CE=2 a,AF=3 a,BF=a 在 Rt CDE 中，DE2=CD2+CE2=(4a)2+(2 a)2=20 a2 同理 EF2=5a2,DF2=25a2 在DEF 中，EF2+DE2=5a2+20a2=25a2=DF2 DEF 是直角三角形，且 DEF=90 .注：本题利用了四次勾股定理，是掌握勾股定理的必练习题。题型四：利用勾股定理求线段长度例题 4 如图 4，已知长方形ABCD 中 AB

42、=8cm,BC=10cm,在边 CD 上取一点 E，将 ADE 折叠使点 D 恰好落在 BC 边上的点 F，求 CE 的长.解析：解题之前先弄清楚折叠中的不变量。合理设元是关键。详细解题过程如下：解：根据题意得Rt ADE Rt AEF AFE=90 ,AF=10cm,EF=DE 设 CE=xcm，则 DE=EF=CD CE=8 x 文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

43、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

44、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

45、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

46、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6

47、S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

48、N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6_ 精品资料在 Rt A

49、BF 中由勾股定理得：AB2+BF2=AF2，即 82+BF2=102，BF=6cm CF=BC BF=10 6=4(cm)在 Rt ECF 中由勾股定理可得：EF2=CE2+CF2，即(8x)2=x2+42 6416x+x2=2+16 x=3(cm),即 CE=3 cm 注：本题接下来还可以折痕的长度和求重叠部分的面积。题型五：利用勾股定理逆定理判断垂直例题 5 如图 5，王师傅想要检测桌子的表面AD 边是否垂直与AB 边和 CD 边，他测得 AD=80cm，AB=60cm，BD=100cm，AD 边与 AB 边垂直吗？怎样去验证AD 边与 CD 边是否垂直？解析：由于实物一般比较大，长度不

50、容易用直尺来方便测量。我们通常截取部分长度来验证。如图4，矩形 ABCD 表示桌面形状，在AB 上截取 AM=12cm,在 AD 上截取 AN=9cm(想想为什么要设为这两个长度？)，连结 MN，测量 MN 的长度。文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1N3N2H8J6文档编码:CY3V6R6S3D9 HE4R9I6G5V9 ZI1

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关键词：: 2022年勾股定理知识点总结2 2022 勾股定理知识点总结

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