初中数学竞赛辅导几何变换(旋转)

第2讲几何变换——旋转典型例题【例1】 C是线段AE上的点，以AC、CE为边在线段 AE的同侧作等边三角形 ABC、CDE，设AD的中点是M，BE的中点是N，连结MN、MC、NC，求证：△CMN是等边三角形．BN DMA C E【例2】如图，两个正方形ABCD和AKLM有一个公共点A．求证：这两个正方形的中心以及线段BM，DK的中点是某正方形的顶点．DQKCP LRAB M-------1 【例3】已知：如图， △ABC、△CDE、△EHK都在等边三角形，且 A、D、K共线， ADDK．求证：△HBD也是等边三角形． E C B A D K H【例4】 △ABC是等边三角形， P是AB边的中点，Q是AC边的中点，R为BC边的中点，M为RC上任意一点，且 △PMS是等边三角形， S与Q在PM的同侧，求证： RMQS． A S P Q B CR M2【例5】 ABCD是正方形，P是ABCD内一点，PA 1，PB 3，PD 7，求正方形 ABCD的面积．A DPB C【例6】 P是等边三角形 ABC内的一点， PA 6，PB 8，PC 10．求△ABC的边长．APB C3【例7】设O是等边△ABC内一点，已知 AOB 115， BOC 125，求以线段OA、OB、OC为边所构成的三角形的各内角大小．【例8】如图，在△ABC中， ACB 90，AC BC，P是△ABC内一点，PA 3，PB 1，PC 2，求 BPC．CPA B【例9】如图，已知△ABC中，A 90，AB AC，D为BC上一点，求证：4BD2 DC2 2AD2．AB D C 【例10】如图，在等腰直角△ABC 中， ACB 90，CA CB，P、Q在斜边AB上，且 PCQ45，求证：PQ 2 AP 2 BQ 2． APQC B【例11】在正方形ABCD中，已知 E、F分别是边BC、CD上的点，满足 EF BE DF，5AE、AF分别与对角线 BD交于M、N．求证：·1）EAF45； （2）MN2 BM2 DN2． A D N F M B E C【例12】如图，在梯形ABCD中，AD∥BC，AD CD，BC CD 2AD，E是CD上一点，且 ABE 45，AD ．求CE的长．A DEB C6 【例13】已知：△ABC中，A≥120 ，P是不与A重合的定点，求证： PAPBPC＞ABAC． AB CP【例14】已知：如图，△ABD是等边三角形， △ABC中，BC a，CA b．问：当 ACB为何值时，C、D两点的距离最大？最大值是多少？CA BD7【例15】已知△ABC，以其各边为底边，向△ABC的外部作等腰三角形使顶角都等于120，求证：△DEF是正三角形．FAABD、BCE、CAF，CEBD【例16】已知：△ABC是锐角三角形，三边长分别是 a、b、c，O是△ABC内的一点，AOB BOC COA 120，OA u，OB v，OC w，△DEF是等边三角形，P是△DEF内一点，PD a，PE b，PF c．求证：△DEF的边长等于u v w．8【例17】已知：三条平行直线 l、m、n，求证：存在一个等边三角形 ABC，使顶点A、B、C分别在l、m、n上．作业 1.已知：ABCD是正方形，O是其中心，OEFG也是正方形，两个正方形的边长都是 a，OG、 OE分别交CD、BC于H、K．求证：SOKCH 1 a2． 4 A DGO HB K CFE2. 已知：如图， ABCD是正方形， 1 2．求证：BE DF AE．A D12FB E C3. △ABC是等边三角形， P是其内的一点， PA 3，PB 4，PC 5，求△ABC的面积．94.P是等边△ABC内部一点，APB、BPC、CPA的大小之比是5:6:7，求以PA、PB、PC为边的三角形的三个角的大小之比． 5.等边△ABC的边长a25 123，点P是△ABC内一点，且PA2 PB2 PC2，若 PC5，求PA、PB的长． 6.在梯形 ABCD中，AD∥BC（BC＞AD），D 90，BCCD12 ，E在CD上， ABE 45，若AE10，求CE的长． A DEB C 7.如图，P、 Q是边长为1的正方形ABCD内两点，使得PAQ PCQ45．求 SPAB S PCQ SQA的值． D A DQPB C10https://wenku.baidu.com/view/9ef06ea3162ded630b1c59eef8c75fbfc77d94d1.htmlhttps://wenku.baidu.com/view/c35231049f3143323968011ca300a6c30d22f144.htmlhttps://wenku.baidu.com/view/1a703220112de2bd960590c69ec3d5bbfc0ada40.htmlhttps://wenku.baidu.com/view/4848d01f77eeaeaad1f34693daef5ef7bb0d12d0.htmlhttps://wenku.baidu.com/view/f0866c4fb1717fd5360cba1aa8114431b80d8e36.htmlhttps://wenku.baidu.com/view/fc6c40dd15791711cc7931b765ce05087732751b.htmlhttps://wenku.baidu.com/view/d6f63182a6c30c2258019e68.htmlhttps://wenku.baidu.com/view/58fa298091c69ec3d5bbfd0a79563c1ec5dad79c.htmlhttps://wenku.baidu.com/view/31aabdc553ea551810a6f524ccbff121dc36c5d1.htmlhttps://wenku.baidu.com/view/7986fbc57dd184254b35eefdc8d376eeafaa170d.htmlhttps://wenku.baidu.com/view/d3cf583f32d4b14e852458fb770bf78a64293a65.htmlhttps://wenku.baidu.com/view/b3d301896d175f0e7cd184254b35eefdc8d315a7.htmlhttps://wenku.baidu.com/view/047e65580622192e453610661ed9ad51f01d54b9.htmlhttps://wenku.baidu.com/view/372e1d86df80d4d8d15abe23482fb4daa48d1d52.htmlhttps://wenku.baidu.com/view/1d40b8fb0a4e767f5acfa1c7aa00b52acfc79caa.htmlhttps://wenku.baidu.com/view/5701d207178884868762caaedd3383c4bb4cb4c6.htmlhttps://wenku.baidu.com/view/a2457ee7bb1aa8114431b90d6c85ec3a86c28b2d.htmlhttps://wenku.baidu.com/view/fbfb2e871fd9ad51f01dc281e53a580217fc50ff.htmlhttps://wenku.baidu.com/view/45d959a35122aaea998fcc22bcd126fff7055db9.htmlhttps://wenku.baidu.com/view/09660edbce84b9d528ea81c758f5f61fb636285e.htmlhttps://wenku.baidu.com/view/67a1c28cbc64783e0912a21614791711cc7979f9.htmlhttps://wenku.baidu.com/view/7159dc846ad97f192279168884868762caaebba1.htmlhttps://wenku.baidu.com/view/c5ded9355122aaea998fcc22bcd126fff6055d06.htmlhttps://wenku.baidu.com/view/703b17544128915f804d2b160b4e767f5acf80c9.htmlhttps://wenku.baidu.com/view/c7bdc607afaad1f34693daef5ef7ba0d4b736d06.htmlhttps://wenku.baidu.com/view/0970d5e753ea551810a6f524ccbff121dc36c509.htmlhttps://wenku.baidu.com/view/f5a3b796bfd5b9f3f90f76c66137ee06eef94e1e.htmlhttps://wenku.baidu.com/view/c0f0cccabfd5b9f3f90f76c66137ee06eef94ee5.htmlhttps://wenku.baidu.com/view/6dded6508ad63186bceb19e8b8f67c1cfad6eee0.htmlhttps://wenku.baidu.com/view/43566ad7a66e58fafab069dc5022aaea988f4129.htmlhttps://wenku.baidu.com/view/2197c42e294ac850ad02de80d4d8d15abe2300b1.htmlhttps://wenku.baidu.com/view/118e36efa200a6c30c22590102020740bf1ecd88.htmlhttps://wenku.baidu.com/view/a0ecca689a89680203d8ce2f0066f5335b816755.htmlhttps://wenku.baidu.com/view/f5a1fea6657d27284b73f242336c1eb91a3733eb.htmlhttps://wenku.baidu.com/view/d24fde7118e8b8f67c1cfad6195f312b3069eb35.htmlhttps://wenku.baidu.com/view/d012dfd930b765ce0508763231126edb6f1a76f2.htmlhttps://wenku.baidu.com/view/7021ab50250c844769eae009581b6bd97f19bc99.htmlhttps://wenku.baidu.com/view/61934e47900ef12d2af90242a8956bec0975a59a.htmlhttps://wenku.baidu.com/view/fae37fa951e2524de518964bcf84b9d529ea2c20.htmlhttps://wenku.baidu.com/view/0c9459b859fb770bf78a6529647d27284a733726.htmlhttps://wenku.baidu.com/view/ff802b704bfe04a1b0717fd5360cba1aa9118c38.htmlhttps://wenku.baidu.com/view/c1f27c73710abb68a98271fe910ef12d2bf9a9d1.htmlhttps://wenku.baidu.com/view/19d787a6f011f18583d049649b6648d7c1c708ae.htmlhttps://wenku.baidu.com/view/55e5d993f56527d3240c844769eae009581ba2a1.htmlhttps://wenku.baidu.com/view/be435152ac51f01dc281e53a580216fc700a53e1.htmlhttps://wenku.baidu.com/view/8af3ff25d4bbfd0a79563c1ec5da50e2534dd14a.htmlhttps://wenku.baidu.com/view/910aaff1b42acfc789eb172ded630b1c58ee9bef.htmlhttps://wenku.baidu.com/view/2fd66598df80d4d8d15abe23482fb4daa48d1d70.htmlhttps://wenku.baidu.com/view/328fe3eb4b7302768e9951e79b89680202d86b0f.htmlhttps://wenku.baidu.com/view/26edf8bd2a160b4e767f5acfa1c7aa00b42a9df2.htmlhttps://wenku.baidu.com/view/d450610c710abb68a98271fe910ef12d2bf9a912.htmlhttps://wenku.baidu.com/view/ca2d8beb4b7302768e9951e79b89680202d86b91.htmlhttps://wenku.baidu.com/view/da94371c85868762caaedd3383c4bb4cf6ecb7d3.htmlhttps://wenku.baidu.com/view/f4a5ee3d6429647d27284b73f242336c1fb93034.htmlhttps://wenku.baidu.com/view/4870f785ae1ffc4ffe4733687e21af45b207fe66.htmlhttps://wenku.baidu.com/view/105e02fd26d3240c844769eae009581b6bd9bd95.htmlhttps://wenku.baidu.com/view/fe084b894531b90d6c85ec3a87c24028915f85fa.htmlhttps://wenku.baidu.com/view/a1bda07e91c69ec3d5bbfd0a79563c1ec5dad72a.htmlhttps://wenku.baidu.com/view/cd6c13f29a6648d7c1c708a1284ac850ac020403.htmlhttps://wenku.baidu.com/view/ff40aa3d370cba1aa8114431b90d6c85ed3a884b.htmlhttps://wenku.baidu.com/view/7de16e09988fcc22bcd126fff705cc1754275ff7.htmlhttps://wenku.baidu.com/view/8890b2d15b8102d276a20029bd64783e08127d89.htmlhttps://wenku.baidu.com/view/01fb408952d380eb63946d29.htmlhttps://wenku.baidu.com/view/2278e49e360cba1aa811da50.htmlhttps://wenku.baidu.com/view/9b4cb8de102de2bd960588a9.htmlhttps://wenku.baidu.com/view/7715c4bd185f312b3169a45177232f60ddcce725.htmlhttps://wenku.baidu.com/view/a95f70f7a66e58fafab069dc5022aaea988f41c1.htmlhttps://wenku.baidu.com/view/1d4bb514f71fb7360b4c2e3f5727a5e9846a273f.htmlhttps://wenku.baidu.com/view/f0903ebe03020740be1e650e52ea551811a6c923.htmlhttps://wenku.baidu.com/view/939350e0a9956bec0975f46527d3240c8547a15c.htmlhttps://wenku.baidu.com/view/f8224dbae55c3b3567ec102de2bd960591c6d96f.htmlhttps://wenku.baidu.com/view/341fd24b80c758f5f61fb7360b4c2e3f5627253d.htmlhttps://wenku.baidu.com/view/b862a0bf77eeaeaad1f34693daef5ef7bb0d125a.htmlhttps://wenku.baidu.com/view/2f654b4481eb6294dd88d0d233d4b14e84243e5f.htmlhttps://wenku.baidu.com/view/12a04191b9f3f90f76c61be0.htmlhttps://wenku.baidu.com/view/a7f89e0828ea81c759f5785c.htmlhttps://wenku.baidu.com/view/46cf416f0a4e767f5acfa1c7aa00b52acfc79cad.htmlhttps://wenku.baidu.com/view/728ed17ad05abe23482fb4daa58da0116c171fe1.htmlhttps://wenku.baidu.com/view/1cf4252cf242336c1fb95e3e.htmlhttps://wenku.baidu.com/view/928e3995c281e53a5902ff6d.htmlhttps://wenku.baidu.com/view/b9cf5977cbaedd3383c4bb4cf7ec4afe04a1b10e.htmlhttps://wenku.baidu.com/view/eb526da69fc3d5bbfd0a79563c1ec5da50e2d6e9.htmlhttps://wenku.baidu.com/view/dbde1df3770bf78a64295407.htmlhttps://wenku.baidu.com/view/ae494d15915f804d2b16c1cd.htmlhttps://wenku.baidu.com/view/5a21ccd2970590c69ec3d5bbfd0a79563c1ed42a.htmlhttps://wenku.baidu.com/view/15a119fa15791711cc7931b765ce0508773275ce.htmlhttps://wenku.baidu.com/view/24e98bcddbef5ef7ba0d4a7302768e9951e76e28.htmlhttps://wenku.baidu.com/view/5e8c6810910ef12d2af9e7f8.htmlhttps://wenku.baidu.com/view/63c821124028915f814dc2c6.htmlhttps://wenku.baidu.com/view/46f403c551e79b89680226db.htmlhttps://wenku.baidu.com/view/1147964983c4bb4cf6ecd161.htmlhttps://wenku.baidu.com/view/4768bef959fafab069dc5022aaea998fcd22405c.htmlhttps://wenku.baidu.com/view/3960fd8f974bcf84b9d528ea81c758f5f61f2995.htmlhttps://wenku.baidu.com/view/8294138b524de518964b7db2.htmlhttps://wenku.baidu.com/view/9c8b8466998fcc22bdd10d30.htmlhttps://wenku.baidu.com/view/a3be58d64a35eefdc8d376eeaeaad1f347931132.htmlhttps://wenku.baidu.com/view/31e45613a200a6c30c22590102020740be1ecdca.htmlhttps://wenku.baidu.com/view/45033ee0172ded630b1cb6d5.htmlhttps://wenku.baidu.com/view/d40b1b9e6c85ec3a87c2c5cb.htmlhttps://wenku.baidu.com/view/2bbb0725b8d528ea81c758f5f61fb7360a4c2bc3.htmlhttps://wenku.baidu.com/view/d5d8de59fd4ffe4733687e21af45b307e871f9ab.htmlhttps://wenku.baidu.com/view/45033ee0172ded630b1cb6d5.htmlhttps://wenku.baidu.com/view/d40b1b9e6c85ec3a87c2c5cb.htmlhttps://wenku.baidu.com/view/60c84f68900ef12d2af90242a8956bec0975a5b0.htmlhttps://wenku.baidu.com/view/fffccdfca88271fe910ef12d2af90242a995abda.htmlhttps://wenku.baidu.com/view/4ee21e99bf1e650e52ea551810a6f524cdbfcbe8.htmlhttps://wenku.baidu.com/view/8e7801d68f9951e79b89680203d8ce2f006665fa.htmlhttps://wenku.baidu.com/view/e66028c2ac02de80d4d8d15abe23482fb4da02ec.htmlhttps://wenku.baidu.com/view/8e6e081e7d1cfad6195f312b3169a4517623e53e.htmlhttps://wenku.baidu.com/view/fb344425760bf78a6529647d27284b73f24236bf.htmlhttps://wenku.baidu.com/view/88e0462b0408763231126edb6f1aff00bfd5706d.htmlhttps://wenku.baidu.com/view/9e1e348fb8f67c1cfbd6b859.htmlhttps://wenku.baidu.com/view/d90a0baa7e21af45b207a80a.htmlhttps://wenku.baidu.com/view/22fbf2f4aff8941ea76e58fafab069dc5122475b.htmlhttps://wenku.baidu.com/view/1e27bea5f011f18583d049649b6648d7c0c70861.htmlhttps://wenku.baidu.com/view/377e57f21611cc7931b765ce05087632311274a2.htmlhttps://wenku.baidu.com/view/056519a34a73f242336c1eb91a37f111f1850df2.htmlhttps://wenku.baidu.com/view/3209e91124c52cc58bd63186bceb19e8b8f6ecbc.htmlhttps://wenku.baidu.com/view/1c1743dc814d2b160b4e767f5acfa1c7aa008292.htmlhttps://wenku.baidu.com/view/4823c4ba3868011ca300a6c30c2259010202f3ca.htmlhttps://wenku.baidu.com/view/d2d66cbe2a160b4e767f5acfa1c7aa00b42a9d2c.htmlhttps://wenku.baidu.com/view/d2d66cbe2a160b4e767f5acfa1c7aa00b42a9d2c.htmlhttps://wenku.baidu.com/view/070736cc7275a417866fb84ae45c3b3566ecdd42.htmlhttps://wenku.baidu.com/view/3730a6d8dc3383c4bb4cf7ec4afe04a1b071b098.htmlhttps://wenku.baidu.com/view/44ad33ffdcccda38376baf1ffc4ffe473268fd7c.htmlhttps://wenku.baidu.com/view/7ecae80a70fe910ef12d2af90242a8956aecaa7a.htmlhttps://wenku.baidu.com/view/c86792e8a9114431b90d6c85ec3a87c241288a0f.htmlhttps://wenku.baidu.com/view/a77fd3fab5daa58da0116c175f0e7cd185251860.htmlhttps://wenku.baidu.com/view/262173a35bcfa1c7aa00b52acfc789eb162d9e1a.htmlhttps://wenku.baidu.com/view/b6b6e6ecf011f18583d049649b6648d7c1c708ba.htmlhttps://wenku.baidu.com/view/8bb8a711b8d528ea81c758f5f61fb7360a4c2bd9.htmlhttps://wenku.baidu.com/view/01f8ffe1f4335a8102d276a20029bd64793e620e.htmlhttps://wenku.baidu.com/view/f5a55e4b8ad63186bceb19e8b8f67c1cfad6eebe.htmlhttps://wenku.baidu.com/view/764d36e2bfd5b9f3f90f76c66137ee06eef94e68.htmlhttps://wenku.baidu.com/view/b30314645ff7ba0d4a7302768e9951e79a89694d.htmlhttps://wenku.baidu.com/view/a220344ecd7931b765ce0508763231126edb77e9.htmlhttps://wenku.baidu.com/view/eceab963ed3a87c24028915f804d2b160a4e869f.htmlhttps://wenku.baidu.com/view/34b4e253d1d233d4b14e852458fb770bf78a3baa.htmlhttps://wenku.baidu.com/view/233b6ae6fc0a79563c1ec5da50e2524de418d007.htmlhttps://wenku.baidu.com/view/49f2f41d88eb172ded630b1c59eef8c75ebf95e2.htmlhttps://wenku.baidu.com/view/5c77925db42acfc789eb172ded630b1c58ee9b5f.htmlhttps://wenku.baidu.com/view/779d328c178884868762caaedd3383c4ba4cb428.htmlhttps://wenku.baidu.com/view/27ed7e196037ee06eff9aef8941ea76e59fa4a90.htmlhttps://wenku.baidu.com/view/bead3f1dafaad1f34693daef5ef7ba0d4b736d20.htmlhttps://wenku.baidu.com/view/915c773080c758f5f61fb7360b4c2e3f56272532.htmlhttps://wenku.baidu.com/view/c7b7518c7dd184254b35eefdc8d376eeafaa1773.htmlhttps://wenku.baidu.com/view/9a564cda590216fc700abb68a98271fe900eafe9.htmlhttps://wenku.baidu.com/view/ba589d21a36925c52cc58bd63186bceb18e8ed15.htmlhttps://wenku.baidu.com/view/1b7357620812a21614791711cc7931b765ce7b22.htmlhttps://wenku.baidu.com/view/0b96f7f7443610661ed9ad51f01dc281e43a56dc.htmlhttps://wenku.baidu.com/view/b8a266ba0a1c59eef8c75fbfc77da26924c59638.htmlhttps://wenku.baidu.com/view/336957dc0722192e4436f67f.htmlhttps://wenku.baidu.com/view/2772c39e001ca300a6c30c22590102020640f266.htmlhttps://wenku.baidu.com/view/ecfa6e3fb8f3f90f76c66137ee06eff9aff849b5.htmlhttps://wenku.baidu.com/view/284f3dc84531b90d6c85ec3a87c24028905f857e.htmlhttps://wenku.baidu.com/view/0034de932f3f5727a5e9856a561252d380eb20b3.htmlhttps://wenku.baidu.com/view/c84d30283d1ec5da50e2524de518964bcf84d294.htmlhttps://wenku.baidu.com/view/059647e011a6f524ccbff121dd36a32d7275c725.htmlhttps://wenku.baidu.com/view/1d94bf22b8f3f90f76c66137ee06eff9aff849da.htmlhttps://wenku.baidu.com/view/6344c4d511661ed9ad51f01dc281e53a5902511c.htmlhttps://wenku.baidu.com/view/bf10bdddb42acfc789eb172ded630b1c58ee9be5.htmlhttps://wenku.baidu.com/view/0473ddc6640e52ea551810a6f524ccbff021ca5a.htmlhttps://wenku.baidu.com/view/e96a579bdb38376baf1ffc4ffe4733687e21fc33.htmlhttps://wenku.baidu.com/view/f30b932e1611cc7931b765ce0508763231127425.htmlhttps://wenku.baidu.com/view/83588e24370cba1aa8114431b90d6c85ed3a884a.htmlhttps://wenku.baidu.com/view/71dd9631f6ec4afe04a1b0717fd5360cba1a8dc6.htmlhttps://wenku.baidu.com/view/c94a8002a48da0116c175f0e7cd184254a351b6c.htmlhttps://wenku.baidu.com/view/0c585641876fb84ae45c3b3567ec102de2bddfd5.htmlhttps://wenku.baidu.com/view/29e17ab1182e453610661ed9ad51f01dc3815708.htmlhttps://wenku.baidu.com/view/2976889559fafab069dc5022aaea998fcd224032.htmlhttps://wenku.baidu.com/view/71360ba8b80d6c85ec3a87c24028915f804d8490.htmlhttps://wenku.baidu.com/view/71360ba8b80d6c85ec3a87c24028915f804d8490.htmlhttps://wenku.baidu.com/view/7550682f814d2b160b4e767f5acfa1c7aa0082b8.htmlhttps://wenku.baidu.com/view/23c4828e59fb770bf78a6529647d27284a733765.htmlhttps://wenku.baidu.com/view/b27f177f2bf90242a8956bec0975f46527d3a795.htmlhttps://wenku.baidu.com/view/b8bf2284a9114431b90d6c85ec3a87c241288a03.htmlhttps://wenku.baidu.com/view/8bbc81770875f46527d3240c844769eae009a394.htmlhttps://wenku.baidu.com/view/0d1c3041250c844769eae009581b6bd97e19bc5d.htmlhttps://wenku.baidu.com/view/2e23ee90f4335a8102d276a20029bd64793e6252.htmlhttps://wenku.baidu.com/view/44a293f5abea998fcc22bcd126fff705cd175c04.htmlhttps://wenku.baidu.com/view/d5c7b0d659fb770bf78a6529647d27284a73372a.htmlhttps://wenku.baidu.com/view/7be5bba5ef06eff9aef8941ea76e58fafab045e4.htmlhttps://wenku.baidu.com/view/2add9cbe66ec102de2bd960590c69ec3d4bbdb5c.htmlhttps://wenku.baidu.com/view/a0d91d59773231126edb6f1aff00bed5b9f37339.htmlhttps://wenku.baidu.com/view/78dbc508846a561252d380eb6294dd88d1d23d8c.htmlhttps://wenku.baidu.com/view/8b03ea44cf2f0066f5335a8102d276a2002960cf.htmlhttps://wenku.baidu.com/view/0a0ea4b8cdbff121dd36a32d7375a417876fc115.htmlhttps://wenku.baidu.com/view/f70ff8b7657d27284b73f242336c1eb91b373372.htmlhttps://wenku.baidu.com/view/333ec0dccd22bcd126fff705cc17552706225e76.htmlhttps://wenku.baidu.com/view/7f8404f82e60ddccda38376baf1ffc4fff47e2e0.htmlhttps://wenku.baidu.com/view/4c034191c950ad02de80d4d8d15abe23492f032c.htmlhttps://wenku.baidu.com/view/4c034191c950ad02de80d4d8d15abe23492f032c.htmlhttps://wenku.baidu.com/view/c7a419a1590216fc700abb68a98271fe910eaf90.htmlhttps://wenku.baidu.com/view/9e92d24268dc5022aaea998fcc22bcd127ff420b.htmlhttps://wenku.baidu.com/view/820d3184fd4ffe4733687e21af45b307e971f953.htmlhttps://wenku.baidu.com/view/11a5bce2c950ad02de80d4d8d15abe23482f03fd.htmlhttps://wenku.baidu.com/view/4abc89872379168884868762caaedd3382c4b555.htmlhttps://wenku.baidu.com/view/1cce419f6ad97f192279168884868762cbaebb1d.htmlhttps://wenku.baidu.com/view/930e21d0580102020740be1e650e52ea5418ceee.htmlhttps://wenku.baidu.com/view/2f7153fef68a6529647d27284b73f242326c312e.htmlhttps://wenku.baidu.com/view/5dd56398a88271fe910ef12d2af90242a995ab81.htmlhttps://wenku.baidu.com/view/bbb5aad6777f5acfa1c7aa00b52acfc788eb9f6d.htmlhttps://wenku.baidu.com/view/d6ca97d417fc700abb68a98271fe910ef02dae96.htmlhttps://wenku.baidu.com/view/b04133b2657d27284b73f242336c1eb91b373337.htmlhttps://wenku.baidu.com/view/70bad92b793e0912a21614791711cc7931b778b3.htmlhttps://wenku.baidu.com/view/60e35fb759fafab069dc5022aaea998fcd224086.htmlhttps://wenku.baidu.com/view/3489d34f4128915f804d2b160b4e767f5bcf8010.htmlhttps://wenku.baidu.com/view/0895d1c1a66e58fafab069dc5022aaea988f411d.htmlhttps://wenku.baidu.com/view/05a44dfa03768e9951e79b89680203d8cf2f6a63.htmlhttps://wenku.baidu.com/view/9c7efbffa31614791711cc7931b765ce04087a7f.htmlhttps://wenku.baidu.com/view/286bf5944b7302768e9951e79b89680202d86b64.htmlhttps://wenku.baidu.com/view/286bf5944b7302768e9951e79b89680202d86b64.htmlhttps://wenku.baidu.com/view/ad44758fcbaedd3383c4bb4cf7ec4afe05a1b1e1.htmlhttps://wenku.baidu.com/view/aab67cc8590216fc700abb68a98271fe900eaf7b.htmlhttps://wenku.baidu.com/view/feb0785eba4cf7ec4afe04a1b0717fd5370cb24f.htmlhttps://wenku.baidu.com/view/4b83487603d276a20029bd64783e0912a3167cf6.htmlhttps://wenku.baidu.com/view/502aacf7a7c30c22590102020740be1e640ecc7c.htmlhttps://wenku.baidu.com/view/2936b3b9b8f3f90f76c66137ee06eff9aef849f3.htmlhttps://wenku.baidu.com/view/5202ba03f9c75fbfc77da26925c52cc58ad6905d.htmlhttps://wenku.baidu.com/view/775705f1fbd6195f312b3169a45177232e60e4de.htmlhttps://wenku.baidu.com/view/22a7fcd62f3f5727a5e9856a561252d381eb207d.htmlhttps://wenku.baidu.com/view/452f10fc78563c1ec5da50e2524de518974bd3da.htmlhttps://wenku.baidu.com/view/54411fd786c24028915f804d2b160b4e777f81e3.htmlhttps://wenku.baidu.com/view/f81b6c1b82d049649b6648d7c1c708a1284a0af9.htmlhttps://wenku.baidu.com/view/9049a4fdf68a6529647d27284b73f242326c31f8.htmlhttps://wenku.baidu.com/view/22a7fcd62f3f5727a5e9856a561252d381eb207d.htmlhttps://wenku.baidu.com/view/b2b7f6300d22590102020740be1e650e53eacffb.htmlhttps://wenku.baidu.com/view/efa68c70541810a6f524ccbff121dd36a22dc412.htmlhttps://wenku.baidu.com/view/2338484c32d4b14e852458fb770bf78a64293a1e.htmlhttps://wenku.baidu.com/view/d1a022822379168884868762caaedd3382c4b544.htmlhttps://wenku.baidu.com/view/49b1358815791711cc7931b765ce050877327510.htmlhttps://wenku.baidu.com/view/a406f3e4a31614791711cc7931b765ce04087a7e.htmlhttps://wenku.baidu.com/view/77de8847ac51f01dc281e53a580216fc710a5307.htmlhttps://wenku.baidu.com/view/d8ef04f59a6648d7c1c708a1284ac850ad020481.htmlhttps://wenku.baidu.com/view/842b6477162ded630b1c59eef8c75fbfc67d94d8.htmlhttps://wenku.baidu.com/view/d284da8bbfd5b9f3f90f76c66137ee06eef94e78.htmlhttps://wenku.baidu.com/view/0c776edb68eae009581b6bd97f1922791788be49.htmlhttps://wenku.baidu.com/view/3825be08dc88d0d233d4b14e852458fb760b383a.htmlhttps://wenku.baidu.com/view/0d1a115b5ebfc77da26925c52cc58bd6308693c0.htmlhttps://wenku.baidu.com/view/bf07da4c48649b6648d7c1c708a1284ac950054f.htmlhttps://wenku.baidu.com/view/4f26f3e454270722192e453610661ed9ac515547.htmlhttps://wenku.baidu.com/view/3bf9111e0875f46527d3240c844769eae109a30e.htmlhttps://wenku.baidu.com/view/bf07da4c48649b6648d7c1c708a1284ac950054f.htmlhttps://wenku.baidu.com/view/1f16bc71541810a6f524ccbff121dd36a32dc4e5.htmlhttps://wenku.baidu.com/view/ec0cb2f7bdd126fff705cc1755270722182e5909.htmlhttps://wenku.baidu.com/view/6da8c1f2a55177232f60ddccda38376bae1fe04e.htmlhttps://wenku.baidu.com/view/3867e4e554270722192e453610661ed9ac515505.htmlhttps://wenku.baidu.com/view/9c973fe40a4e767f5acfa1c7aa00b52acec79c9d.htmlhttps://wenku.baidu.com/view/1d2b5983492fb4daa58da0116c175f0e7dd11943.htmlhttps://wenku.baidu.com/view/cd0027ee5e0e7cd184254b35eefdc8d3