初二数学矩形折叠问题 初二数学矩形纸片折叠问题
\u521d\u4e8c\u6570\u5b66\u77e9\u5f62\u6298\u53e0\u95ee\u9898\uff0c\u6c42\u6551\uff01(1)\u25b3BMP\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62
\u8bc1\u660e\uff1a
\u8fde\u63a5AN
\u2235EF\u5782\u76f4\u5e73\u5206AB
\u2234AN\uff1dBN
\u7531\u6298\u53e0\u7684\u6027\u8d28\u53ef\u77e5\uff1a
AB\uff1dBN\uff0c\u2220ABM\uff1d\u2220MBN\uff0c\u2220BNM\uff1d\u2220A\uff1d90\u00b0
\u2234AN\uff1dAB\uff1dBN
\u2234\u25b3ABN\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62
\u2234\u2220ABN\uff1d60\u00b0
\u2234\u2220ABM\uff1dMBN\uff1d1/2\u2220ABN\uff1d30\u00b0
\u2220NBP\uff1d\u2220ABC\uff0d\u2220ABN\uff1d30\u00b0
\u2234\u2220BPN\uff1d\u2220BNM\uff0d\u2220NBP\uff1d60\u00b0
\u2220MBP\uff1d\u2220MBN\uff0b\u2220NBP\uff1d60\u00b0
\u2234\u2220BMP\uff1d60\u00b0
\u2234\u2220BPN\uff1d\u2220MBP\uff1d\u2220BMP\uff1d60\u00b0
\u2234\u25b3BMP\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62
(2)
\u8981\u5728\u77e9\u5f62\u7eb8\u7247ABCD\u4e0a\u526a\u51fa\u7b49\u8fb9\u25b3BMP\uff0c\u5219BC\u2265BP
\u5728Rt\u25b3BNP\u4e2d\uff0cBN\uff1dAB\uff1da\uff0c\u2220NBP\uff1d30\u00b0
\u2234cos\u2220NBP\uff1dBN/BP\uff1d\u221a3/2\uff0cBP\uff1dBN/(\u221a3/2)\uff1da/(\u221a3/2)
BC\u2265BP\uff0cb\u2265a/(\u221a3/2)
\u2234a\u2264\u221a3/2 b
\u2234\u5f53a\u2264\u221a3/2 b\u65f6\uff0c\u5728\u77e9\u5f62ABCD\u4e0a\u80fd\u526a\u51fa\u8fd9\u6837\u7684\u7b49\u8fb9\u25b3BMP
(3)
\u2235\u2220M'BC\uff1d60\u00b0
\u2234\u2220ABM'\uff1d90\u00b0\uff0d60\u00b0\uff1d30\u00b0
\u5728Rt\u25b3ABM'\u4e2d\uff0ctan\u2220ABM'\uff1dAM'/AB
\u2234tan30\u00b0\uff1dAM'/2
\u2234AM'\uff1d2\u00d7(\u221a3/3)\uff1d2\u221a3/3
\u2234M'\u7684\u5750\u6807\u4e3a(2\u221a3/3\uff0c2)
\u2235M'\u5728BM'(y\uff1dkx)\u4e0a
\u22342\uff1d2\u221a3/3k
\u89e3\u5f97k\uff1d\u221a3
\u5047\u8bbe\u25b3ABM' \u6cbfBM\u2032\u6298\u53e0\u540e\uff0c\u70b9A\u843d\u5728\u77e9\u5f62ABCD\u5185\u7684\u70b9\u4e3aA\u2032
\u8fc7A'\u4f5cA'H\u22a5BC\u4ea4BC\u4e8eH\uff0c
\u2235\u25b3A\u2018BM'\u224c\u25b3ABM\u2019
\u2234\u2220A'BM'\uff1d\u2220ABM'\uff1d30\u00b0\uff0cA'B\uff1dAB\uff1d2
\u2234\u2220A'BH\uff1dM'BC\uff0d\u2220A'BM'\uff1d30\u00b0
\u5728Rt\u25b3A'BH\u4e2d\uff0c\u2220A'BH\uff1d30\u00b0
\u2234A'H\uff1d1/2A'B\uff1d1(30\u00b0\u6240\u5bf9\u7684\u76f4\u89d2\u8fb9\u7b49\u4e8e\u659c\u8fb9\u7684\u4e00\u534a)\uff0cBH\uff1d\u221a3
\u2234A'\u7684\u5750\u6807\u4e3a(\u221a3\uff0c1)
\u2234\u70b9A\u843d\u5728EF\u4e0a
\u505a\u8f85\u52a9\u7ebfFG\u5782\u76f4CD\u4e8eF\u70b9 \u4ea4AB\u4e8eG\u70b9
\u2220ABE=\u2220EBC
\u2220EBF=\u2220FBC
\u56e0\u4e3a\u2220ABE=\u2220EBC=45\u00b0
\u6240\u4ee5\u2220EBF=\u2220FBC=22.5\u00b0
\u2220GFB=\u2220FBC=22.5\u00b0
\u2220DFB=\u2220DFG+\u2220GFB=90\u00b0+22.5\u00b0=112.5\u00b0
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绛旓細鐭╁舰缈绘姌鍚庢槗鐭F=FC锛屽埄鐢ㄧ洿瑙掍笁瑙掑舰BFC锛岀敤鍕捐偂瀹氱悊姹傚嚭CF闀匡紝涔熷氨鏄疉F闀匡紝S鈻矨FC= 1/2AF•BC锛庤В绛旓細瑙ｏ細璁続F=x锛屼緷棰樻剰鍙煡锛岀煩褰㈡部瀵硅绾緼C瀵规姌鍚庢湁 鈭燚鈥=鈭燘=90掳锛屸垹AFD鈥=鈭燙FB锛孊C=AD鈥测埓鈻矨D鈥睩鈮屸柍CBF 鈭碈F=AF=x鈭碆F=8-x 鍦≧t鈻矪CF涓湁BC2+BF2=FC2 鍗4^2+...
绛旓細姊舰ABEF鐨勪腑浣嶇嚎鏄疢B'銆傛墍浠B'=FB'銆
绛旓細鍏堟彁浜3灏忛鐨勮В绛旓紝鐧藉ぉ璇风户缁拷闂.
绛旓細鐢鎶樺彔寰楋細鈭燚EF=鈭燘EF 鈭礎D鈭C(鐭╁舰)鈭粹垹DEF=鈭燘FE锛屸埓鈭燘EF =鈭燘FE 鈭碆E=BF 鈭礏E=DE(鎶樺彔) 鈭碊E=BF 鈭村洓杈瑰舰EBFD鏄彵褰 鈭礎D=AE+ED=9 鍙堚埖AB=3 鍦ㄢ柍ABE涓紝鐢卞嬀鑲″畾鐞嗗彲寰桝E=4锛孊E=5 浣淓P涓凚C浜嶱锛屽垯BP=AE=4锛孍P=AD=3锛孭F=5-4=1锛屽湪RT鈻矱FP涓敱鍕捐偂瀹氱悊...
绛旓細鍥犱负鏄鎶樺彔 鎵浠ュ嚭鍏ㄧ瓑...涔熷氨鏄柍BC1D鈮屸柍BCD 搴旇娌闂鍚 閭ｄ箞 鎺ョ潃 鈭礎BCD涓鐭╁舰 鈭碅B=CD=6 BC=AD=8 鈭碨鈻矪CD=2/1*DC*BC =2/1*6*8 =24 鈭碘柍BC1D鈮屸柍BCD 鈭碨鈻矪C1D=S鈻矪CD=24 搴旇娌￠敊鍚 浠呬緵鍙傝
绛旓細鈭礒F鍨傜洿骞冲垎AB锛屸埓AN=BN锛庣敱鎶樺彔鐭B=BN锛屸埓AN=AB=BN锛庘埓鈻矨BN涓虹瓑杈逛笁瑙掑舰锛庘埓鈭燗BN=60掳锛庘埓鈭燩BN=30掳锛庡張鈭碘垹ABM=鈭燦BM=30掳锛屸垹BNM=鈭燗=90掳锛屸埓鈭燘PN=60掳锛屸垹MBP=鈭燤BN+鈭燩BN=60掳锛庘埓鈭燘MP=60掳锛庘埓鈭燤BP=鈭燘MP=鈭燘PM=60掳锛庘埓鈻矪MP涓虹瓑杈逛笁瑙掑舰锛庯紙2锛夎鍦鐭╁舰绾哥墖ABCD...
绛旓細棣栧厛浣犲彲浠ユ嬁涓寮犵焊鎶樹竴涓嬧︿互渚挎洿濂界殑鐞嗚В杩欓亾棰樼洰銆傝DE=X,鍒欏垪鍑哄悇涓竟鐨勯暱搴:鐢鎶樺彔鐭F=AD=8,DE=EF=X,FC=6-X,鎵浠ョ敱鍕捐偂瀹氱悊鍐欏嚭FC,AB=6.鏄庢樉鐪嬪嚭鈻矨BF鈭解柍FDE 鎵浠B:AF=FD:DE 鏈鍚庣敱璁ㄨ姹傚嚭AE=8(4-鈭7)/3 娉:鈭氫负鏍瑰彿 鍛煎懠鈥︾粓浜庡啓瀹屼簡鈥﹀笇鏈涘啓鐨勪笉寰堥毦鎳傚暒鍟﹀暒锝瀆_^绁...
绛旓細瑙ｏ細锛1锛 鈭礜涓築C鐨勪腑鐐 鈭碆N=NC=1/2BC=1/2 鈭碢B=PC 鈭碢N鈯C 鈭粹垹PNC=90掳 鈭鎶樺彔 鈭粹柍PQB鈮孋QB 鈭碢B=CB=1 鈭碢C=1 鈭靛湪鈻砅CN涓紝鈭燩NC=90掳 鈭碢N^2+NC^2=PC ^2 鈭碢N^2+1/4=1 鈭碢N= 鏍瑰彿锛3/4锛夊嵆锛堟牴鍙3锛/2 鈭靛洓杈瑰舰ABCD鏄鏂瑰舰 鈭粹垹D=鈭燚CB=90掳锛孉D鈭...
绛旓細鈭垫鏂瑰舰ABCD 鈭碅D锛滱B锛屸垹BAD锛濃垹B锛90 鈭碅P锛濃垰锛圓B²+BP²锛夛紳鈭氾紙144+25锛夛紳13 鈭电偣A娌縀F鎶樺彔鑷砅 鈭碋F鈯P 鈭粹垹BAP+鈭燗EF锛90 鈭礔G鈯B 鈭鐭╁舰AGFD锛屸垹GFE+鈭燗EF锛90 鈭碐F锛滱D锛屸垹BAP锛濃垹GFE 鈭碐F锛滱B 鈭粹柍ABP鈮屸柍FGE 锛圓SA锛夆埓EF锛滱P锛13 鏁板杈呭鍥㈣В绛斾簡浣...
