在直角梯形ABCD中。AB为梯形的腰。AB=BC=2，AD=1，试着把直角梯形分为四个全等的部分。 如图所示，在直角梯形ABCD中，AB为垂直于底边的腰，AD=...
\uff082013?\u5927\u5e86\uff09\u5982\u56fe\u6240\u793a\uff0c\u5728\u76f4\u89d2\u68af\u5f62ABCD\u4e2d\uff0cAB\u4e3a\u5782\u76f4\u4e8e\u5e95\u8fb9\u7684\u8170\uff0cAD=1\uff0cBC=2\uff0cAB=3\uff0c\u70b9E\u4e3aCD\u4e0a\u5f02\u4e8eC\uff0cD\u7684\u89e3\uff1a\uff081\uff09\u2235S1=12AD?AF=12x\uff0cS3=12BC?BF=12\u00d72\u00d7\uff083-x\uff09=3-x\uff0c\u2234S1S3=12x\uff083-x\uff09=12\uff08-x2+3x\uff09=12[-\uff08x-32\uff092+94]=-12\uff08x-32\uff092+98\uff080\uff1cx\uff1c3\uff09\uff0c\u2234\u5f53x=32\u65f6\uff0cS1S3\u7684\u6700\u5927\u503c\u4e3a98\uff1b\uff082\uff09\u4f5cDM\u22a5BC\uff0c\u5782\u8db3\u4e3aM\uff0cDM\u4e0eEF\u4ea4\u4e0e\u70b9N\uff0c\u2235AFFB=t\uff0c\u2234AF=tFB\uff0c\u2235BM=MC=AD=1\uff0c\u2234NEMC=DNDM=AFAF+FB=tFBtFB+FB=tt+1\uff0c\u2234NE=tt+1\uff0c\u2234EF=FN+NE=1+tt+1=2t+1t+1\uff1b\uff083\uff09\u2235AB=AF+FB=\uff08t+1\uff09FB=3\uff0c\u2234FB=3t+1\uff0c\u2234AF=tFB=3tt+1\uff0c\u2234S1=12AD?AF=12\u00d73tt+1=<table cellpadding="-1" cellspa
\u89e3\uff1a\uff081\uff09\u2235S1=1/2
AD•AF=1/2x\uff0c
S3=1/2
BC•BF=1/2\u00d72\u00d7\uff083-x\uff09=3-x\uff0c
\u2234S1S3=1/2x\uff083-x)=1/2\uff08-x2+3x\uff09=1/2[-\uff08x-3/2\uff092+9/4]=-1/2\uff08x-3/2\uff092+9/8\uff080\uff1cx\uff1c3\uff09\uff0c
\u2234\u5f53x=3/2\u65f6\uff0cS1S3\u7684\u6700\u5927\u503c\u4e3a9/8\uff1b
\uff082\uff09\u4f5cDM\u22a5BC\uff0c\u5782\u8db3\u4e3aM\uff0cDM\u4e0eEF\u4ea4\u4e0e\u70b9N\uff0c
\u2235AF/FB=t\uff0c
\u2234AF=tFB\uff0c
\u2235BM=MC=AD=1\uff0c
\u2234NE/MC=DN/DM=AF/AF+FB=tFB/tFB+FB=t/t+1\uff0c
\u2234NE=t/t+1\uff0c
\u2234EF=FN+NE=1+t/t+1=2t+1/t+1\uff1b
\uff083\uff09\u2235AB=AF+FB=\uff08t+1\uff09FB=3\uff0c
\u2234FB=3/t+1\uff0c
\u2234AF=tFB=3t/t+1\uff0c
\u2234S1=1/2
AD•AF=1/2 x 3t/t+1=3t/2(t+1)\uff0c
S3=1/2
BC•FB=1/2 \u00d72\u00d7 3/t+1=3/t+1\uff1b
S2=1/2
AB•FE=1/2 \u00d73\u00d7 2t+1/t+1=3(2t+1)/2(t+1)\uff0c
\u2234S1S3=9t/2(t+1)^2
\uff0cS2^2=9(2t+1)^2/4(t+1)^2\uff0c
\u22349(2t+1)^2 /4(t+1)^2 =4\u00d79t /2(t+1)^2\uff0c\u53734t2-4t+1=0\uff0c\u89e3\u5f97t=1/2.
\u5f88\u6709\u8bda\u610f\u7684QAQ\uff01\uff01\uff01\u7eaf\u624b\u6253\uff01\uff01\u4e0d\u542b\u590d\u5236\u7c98\u8d34\uff01\uff01\u697c\u4e3b\u4f60\u5c31\u7ed9\u6211\u5206\u5457\uff01\u3010\u6b64\u4eba\u5df2\u6eda\u7c97= =
原梯形ABCD可以分为四个全等的等腰梯形,见下图:
绛旓細锛1锛夆埖 锛 锛 锛 锛2锛夎兘 褰撳洓杈瑰舰PQDC涓哄钩琛屽洓杈瑰舰鏃讹紝鈭礠D=PC鈭 锛3锛変笉鑳斤紝 褰撳洓杈瑰舰PQDC涓虹瓑鑵版褰㈡椂锛孭E=CF 涓嶅悎瀹為檯 锛1锛夋牴鎹細璺▼=閫熷害脳鏃堕棿锛岃〃绀虹嚎娈电殑闀垮害锛屽啀鍒╃敤锛歋 姊舰ABPQ =S 姊舰PQDC 锛屽垪鏂圭▼姹傝В锛涳紙2锛夊彧瑕佽兘婊¤冻DQ=PC鍗冲彲锛岀敱姝ゅ缓绔嬬瓑閲...
绛旓細鈭电焊鐗囨部杩囩偣D鐨勭洿绾挎姌鍙狅紝浣跨偣A钀藉湪杈笴D涓婄殑鐐笶澶勶紝鎶樼棔涓篋F锛屸埓鈭燚EF=鈭燗=90掳锛孌A=DE锛屸埖AB鈭C锛屸埓鈭燗DE=90掳锛屸埓鍥涜竟褰DEF涓虹煩褰紝鑰孌A=DE锛屸埓鍥涜竟褰DEF涓烘鏂瑰舰锛涳紙2锛夆埖DG鈭B锛孌C鈭B锛屸埓鍥涜竟褰GDC鏄钩琛屽洓杈瑰舰锛屸埓BC=DG锛孌C=BG锛屸埓EC鈮燘G锛屸埓鍥涜竟褰GBC鏄褰锛屽張鈭...
绛旓細鈭,鈭燽=90掳,ab=3,bc=4 鈭寸敱鍕捐偂瀹氱悊寰楋細ac=5 鍙堚埖S姊疉BCD=1/2*3*(2+4)=9 S鈻矨BC=1/2*4*3=6 鈭碨鈻矨DC=S姊疉BCD-S鈻矨BC=3 鍙堚埖de鈯c 鈭碨鈻矨DC=1/2*ac*de=3 鍗砫e=6/5
绛旓細瑙ｇ瓟锛氳В锛氾紙1锛変互鐩寸嚎AB涓x杞达紝绾挎AB鐨勪腑鐐逛负鍘熺偣锛屽缓绔嬪鍥炬墍绀虹殑骞抽潰鐩磋鍧愭爣绯伙紝鍒橝(?2锛0)锛孊(2锛0)锛孋(2锛3)锛孌(?2锛3)锛庘︼紙1鍒嗭級鈭礎D+BD=3+5=8锛濧B锛屸埓渚濋鎰忥紝鏇茬嚎娈礑E鏄互A銆丅涓哄乏銆佸彸鐒︾偣锛岄暱杞撮暱涓8鐨勬き鍦嗙殑涓閮ㄥ垎锛 锛3鍒嗭級鏁呮洸绾挎DE鐨勬柟绋嬩负x216+y212锛1(...
绛旓細鐩稿垏銆傚緢绠鍗曠殑銆傝繃鐐笶浣淓F鈯D浜嶧锛屾槗寰楋細EA=EF锛孍B=EF.鈭碋A=EB.鍗崇偣E涓哄渾蹇冧笖绾挎EF涓哄叾鍗婂緞锛岃孍F鈯D.鈭碈D涓鸿鍥殑鍒囩嚎.
绛旓細璇佹槑锛氾紙1锛夎繃鐐笵浣淒M鈯AB锛屸埖DC鈭B锛屸垹CBA=90掳锛屸埓鍥涜竟褰CDM涓虹煩褰紟鈭碊C=MB锛庘埖AB=2DC锛屸埓AM=MB=DC锛庘埖DM鈯B锛屸埓AD=BD锛庘埓鈭燚AB=鈭燚BA锛庘埖EF鈭B锛孍F鈮燗B锛屸埓鍥涜竟褰BFE鏄瓑鑵姊舰锛庤В锛氾紙2锛夆埖DC鈭B锛屸埓鈻矰CF鈭解柍BAF锛庘埓CD/AB=CF/AF=1/2 鈭礐F=4cm锛屸埓AF=8cm锛庘埖AC鈯...
绛旓細(3) 浠涓哄師鐐笵A涓簒杞村缓鐩磋鍧愭爣绯伙紝鍒橠(0,0) C(0, 2鈭3) P( 10-2t,2鈭3) Q(8-t,0) 鍒欐湁鏂圭▼(9-1.5t)^2=( 2-t) ^2 +12 0<t<5
绛旓細璁姊洿瑙掓褰BCD涓锛屸垹B = 90掳 鍦ㄢ柍ABD涓紝鈭燗 = 90掳锛孊D = 15锛孉B = 12锛屸埓BD² = AB²+AD²鈭碅D = 9 鍦≧t鈻矨BC涓紝AC² = AB² + BC²锛孉C = 20锛孉B = 12 鈭碅C² = AB²+ BC²鈭碆C = 16 鈭碨姊舰ABCD = 锛圓D+...
绛旓細杩囩偣D浣淒G鈯B浜庣偣G鈫掑洓杈瑰舰CDBG涓虹煩褰⑩啋BG=CD 鈭 AB=2CD 鈭 AB=2BG 鈭 鐐笹鏃鏄疉B鐨勫瀭瓒冲張鏄腑鐐 DG涓衡柍ABD鐨勪腑鍨傜嚎 鈭 鈻矨BD鏄瓑鑵颁笁瑙掑舰 鈭 EF//AB 鈭 AE=BF 鈭 鍥涜竟褰BFE鏄瓑鑵姊舰
绛旓細棣栧厛杩囩偣O浣淥E鈯D浜D鐨勫欢闀跨嚎浜嶦锛孫E浜も姍O 浜嶱锛屽垯鈻砅CD灏辨槸鎵姹傜殑涓夎褰紝杩炴帴OC銆丱D锛岃繃鐐笵浣淒F鈯C浜庣偣F锛岀敱鐩磋姊舰ABCD涓锛孉D鈭C锛屸垹B=90掳锛孊C=2AB=2AD=4锛庢槗姹傚緱鈻砄CD鐨勯潰绉笌CD鐨勯暱锛岀户鑰屾眰寰桹E鐨勯暱锛屽垯鍙眰寰桺E鐨勯暱锛岀户鑰屾眰寰椻柍CPD鐨勬渶灏忛潰绉紟瑙ｏ細杩囩偣O浣淥E鈯D浜...
