2022年初中数学图形的平移与旋转人教版鲁教版 .pdf

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1、图形的平移和旋转一、知知要点1.图形的平移(1)平移的概念：在平面内，将一个图形沿某个方向移动一定的距离，这样的图形运动称为平移，平移不改变图形的形状和大小。（2）平移的特点：平移是指整个图形平行移动，包括图形的每一条线段，每一个点。经过平移，图形上的每一个点都沿同一个方向移动相同的距离。平移不改变图形的形状、大小，方向，只改变图形的位置。(3)平移的基本性质：经过平移，对应点所连的线段平行且相等，对应线段平行且相等，对应角相等。例题 1：在 ABC的边 BC上，取两点 D、E，使 BD CE，观察 AB AC与 AD AE的大小关系。分析：四条线段 AB、AC、AD、AE比较分散，可利用平移

2、的方法将它们集中到一起，即可求出大小关系。证明：将AEC沿 EB的方向平移到 FBD位置FB AE，FD AC 设 FD与 AB的交点为 O 在AOD 中，AO OD AD 在FOB中，FO OB FB ABFDAOOBFOODAOODFOOBADFBABACADAE例题 2：已知：AB CD 1，AB与 CD交于 O点，DOB 60，比较 AC BD与 1 的大小。分析：利用平移将 AC与 BD集中，再利用三角形三边关系进行比较大小。解：ACBD1证明：过 C作 CE AB，过 B作 BE AC，连结 DE 四边形 ABEC 为平行四边形AC BE，AB CE DOB 60，AB CE DC

3、E 60AB CD 1 CE CD 1 DCE 为等边三角形DE 1 在DEB中，DB BE DE 即 DB AC 1练习：1.两个长为 12cm的线段 AB与 CD相交于点 O，AOD 120，判断 AC BD的最小值2.旋转在平面内，将一个图形绕着一个定点沿某个方向转动一个角度，这样的图形运动称为旋转。这个定点称为旋转中心，转动的角称为旋转角。旋转不改变图形的大小和形状。注意：“将一个图形绕一个定点沿某个方向转动一个角度”意味着图形上的每个点同时都按相同的方式转动相同的角度。在物体绕着一个定点转动时，它的形状和大小不变。因此，旋转具有不改变图形的大小和形状的特征。2旋转的性质（1）对应点到

4、旋转中心的距离相等；（2）对应点与旋转中心所连线段的夹角等于旋转角；（3）旋转前、后的图形全等；（4）图形的旋转由旋转中心和旋转角度决定。例题：例 1.如图，P是正方形 ABCD 内一点，将 ABP绕点 B顺时针旋转 90，使 AB与 CB重合，BP到达 BP处，AP到达 CP处，若 AP的延长线正好经过P，求 APB的度数。文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O

5、7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6

6、V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7

7、R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L

8、2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4

9、N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4

10、P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5文档编码:CQ4U

11、6L2O7X7 HV6F9V4N6V6 ZT10J9D4P7R5分析：此题运用旋转将 ABP绕点 B顺时针旋转 90，根据旋转性质求出 BPC的度数即可。而BPC又是 BPP 与CPP之和，可各个击破，从而得解。解：由旋转的性质及特征可知：PBP90，AP PC，BP BP 在 BPP中，BP PBPP121809045又AP的延长线正好经过P 点APC90BPCAPCBPP135从而可得 APB 135练习：如图，设 P是等边三角形 ABC内的一点，PA=3，PB=4.PC=5，求 APB的度数APCB例 2.已知：如图，E是正方形 ABCD 的边 BC上一点，AF平分 EAD交 CD于点

12、F，说明 AE BE DF的理由。分析：由于要证的 3 条线段 AB、BE、DF分散在两个三角形中，可利用旋转变换，将其放到一个三角形中。解：把ADF绕点 A顺时针旋转 90，则点 D转到了点 B的位置，点 F转到了点 F 的位文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5

13、P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:C

14、G3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5

15、P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:C

16、G3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5

17、P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:C

18、G3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9置，根据旋转的性质得：31，FBFD，AFBAFD ABCD 为正方形DABF90F、B、E、C在一条直线上又 12EAB 9032

19、EAB 90FAE290又 AFD 190AFB19012 FAEAFB AE FEFBBE FD BE 练习题：已知五边形 ABCDE 中，AB=AE,BC DE=CD,BAE=BCD=120，ABC AED=180，连接 AD，求证：AD平分 CDE CBAED例 3.ABC为等边三角形，点D、E、F 分别在边 AC、AB、BC上，且 AE BF CD，连结 AF、BD、CE，分别交于点 G、H、M。（1）求 1 的度数；（2）判断 GMH 的形状。分析：等边三角形是旋转对称图形，且每个角都是60，1 是BCH 的外角，可知 123。而24 14360，从而得证。解：（1）等边 ABC 是

20、旋转对称图形，且AE BF CD 所以，ABC绕旋转中心旋转 120后，AEC、BFA、CDB 能够重合24 由123 文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9

21、文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4

22、L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9

23、文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4

24、L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9

25、文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4

26、L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T914360（2）同理可得：GMH MGH 60GMH 是等边三角形练习题：在多边形 ABCD 中 BC=4，CD=4 AB,AE=DE=6，AE AB,DE CD,则多边形的面积是多少？EDCBA例题 4：已知：如图，E、F、G分别是正方形

27、 ABCD 中 BC、AB、CD上的点，且 AE FG。求证：AE FG 分析：AE、FG所在位置不易证明相等，可将其一改变位置，如可用平移、旋转将其位置改变后再进行证明。证明：延长 AB至 F 使 BFBE，连结 CF 正方形 ABCD AB CB，ABC 90又 CBF90，BE BF ABE绕点 B顺时针旋转 90可得 CBF AE CF，AE CF FG AE FG CF 又正方形 ABCD，AB CD 四边形 GFFC为平行四边形CFFG AE FG 基础练习题：1.如图，四边形 ABCD 是边长为 1 的正方形，且 DE=14，ABF是ADE 的旋转图形文档编码:CG3T7M8R5

28、X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3

29、A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5

30、X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3

31、A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5

32、X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3

33、A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5

34、X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9（1）旋转中心是哪一点？（2）旋转了多少度？（3）AF的长度是多少？（4）如果连结 EF，那么 AEF是怎样的三角形？2如图 ABC中，BAC 90，P是ABC 内一点，将 ABP绕点 A逆时针旋转一定角度后能与 ACQ 重合，如果 AP 3，那么 APQ 的面积是多少？3.在四边形 ABCD 中，ADC ABC 90，AD CD，DP AB于 P，若SABCD25，求 DP的长。3.

35、轴对称图形如果一个图形沿一条直线折叠后，直线两旁的部分能够重合，那么这个图形叫做轴对称图形文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

36、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

37、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

38、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

39、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

40、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

41、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9有的轴对称图形的对称轴不止一条，如圆就有无数条对称轴（1）轴对称有一个图形沿着某一条直线折叠，如果它能够与另一个图形重合，?那么就说这两个图形关于这条直线对称，这条直线叫做对称轴，折叠后重合的点是对应点，叫做对称点两个图形关于直线对称也叫做轴对称&1图形轴对称的性质如果

42、两个图形成轴对称，?那么对称轴是任何一对对应点所连线段的垂直平分线；轴对称图形的对称轴是任何一对对应点所连线段的垂直平分线&2轴对称与轴对称图形的区别轴对称是指两个图形之间的形状与位置关系，?成轴对称的两个图形是全等形；轴对称图形是一个具有特殊形状的图形，把一个轴对称图形沿对称轴分成两个图形，这两个图形是全等形，并且成轴对称&3轴对称变换由一个平面图形得到它的轴对称图形叫做轴对称变换?成轴对称的两个图形中的任何一个可以看着由另一个图形经过轴对称变换后得到&4轴对称变换的性质（1）经过轴对称变换得到的图形与原图形的形状、大小完全一样（2）?经过轴对称变换得到的图形上的每一点都是原图形上的某一点关

43、于对称轴的对称点（3）连接任意一对对应点的线段被对称轴垂直平分轴对称典型图形：等腰三角形、等边三角形&1等腰三角形：有两条边相等的三角形是等腰三角形相等的两条边叫做腰，另一条边叫做底边两腰所夹的角叫做顶角，腰与底边的夹角叫做底角等腰三角形的性质：性质 1：等腰三角形的两个底角相等（简写成“等边对等角”）性质 2:等腰三角形的顶角平分线、底边上的中线、底边上的高互相重合文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

44、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

45、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

46、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

47、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

48、4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X

49、1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A4P1T9文档编码:CG3T7M8R5X1 HT4L2B6K5P8 ZM9W3A

50、4P1T9等腰三角形的判定定理如果一个三角形有两个角相等，那么这两个角所对的边也相等（简写成“等角对等边”）特别的：（1）有一边上的角平分线、中线、高线互相重合的三角形是等腰三角形（2）有两边上的角平分线对应相等的三角形是等腰三角形（3）有两边上的中线对应相等的三角形是等腰三角形（4）有两边上的高线对应相等的三角形是等腰三角形例题 1 如图，在ABC中，AB=AC，A=92，延长 AB到 D，使 BD=BC，连结 DC求D 的度数，ACD的度数DBCA分析：要求解角的度数，必须找到几个角的关系，然后利用三角形内角和为180求解。解：AB=AC,BD=BC ABC=ACB,D=BCD 又 ABC