人教版八下数学全册书精品作课教案

人教版八下数学全册书精品作课教案

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时间:2023-06-28

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24_ᓝWabcdeᦪ17.1.1bcdeᦪḄfg,ஹᦟij᪗1.PinᳮpqrsbcdeᦪḄᭆu2.wᑨy•%{|Ḅeᦪ?ᔲ~bcdeᦪqᵨ|ᦪeᦪp᪆3.w᪷▭⚪FḄᩩ|bcdeᦪḄp᪆eᦪḄஹஹ1.ZᳮpbcdeᦪḄᭆuw᪷:;ᩩᑏeᦪp᪆2.ZᳮpbcdeᦪḄᭆu3.ḄẚZ(1)ᙠᐭbcdeᦪḄᭆu¡〉£¤¥,_11aḄ¦cdeᦪஹ,§eᦪNTᐵ;©ª᪵¬®¯T°±cw²±bcdeᦪᭆuḄᳮp(2)³f´in±bcdeᦪᭆuḄᳮpµ¶y=8,N»¼½?eᦪy,NX»¾½?,%ᑖÀÁOXᙠᑖÃÄÅXḄᢣᦪ?1,ᑖÇ?È~0ḄÊᦪkZµÀÁOxḄÍÎÐᵫxᙠᑖÃÄᦑÍxWOḄ,ᑗᦪÕµeᦪyḄÍÎÐÖ~k#0,Åx#0,ᡠ¬eᦪÎyØÈ¡w~0஺Ùp¡±᯿¦cdeᦪy=kx(kWO),cÛὅp᪆ḄT)ÝÈ)஺(3)v=—(kWO)࡬ᑏᡂy=(kWO)ᡈxy=k(kWO)Ḅ¶.xâஹd⚪Ḅfãᑖ᪆ᦟᩞ_46⚓Ḅὃ⚪?~ᐭbcdeᦪḄᭆuéêëḄjḄ?ìiní▭⚪îïðᐸFḄᦪOᐵÝÁᓄóôõö÷øஹùúஹûüᨬþbcdeᦪḄᭆueᦪḄ஺ᦟᩞ_47⚓Ḅ1⍝ᵨᦪᦪ᪆Ḅ⚪⚪ḄḄ⌕ᦪᭆḄᳮ!"ᦪ᪆Ḅ#$%&'()*ᦪᡠⅾ-Ḅ“/ᓄ12”Ḅ45ᱯ7ᦪ18/9:;Ḅᓫ=2ᐵ஺⊡ᐙ1ஹ2DEFḄ⚪GHIJKLᙢᳮᦪḄᭆ஺⊡ᐙ3⍝Oᔠ⚪⚪ᵨᦪQᵫSTᦪUᔠVᡂḄXḄᦪᐵᨵZ[\H]^ᑖ᪆ஹ`a⚪ḄHb஺cஹdᚪfᐭ1.jklmnoᦪஹpᦪqrsḄtuv᪵Ḅq2.)xdyὁ{|}~n;1ᙳ[Ḅᐵv᪵Ḅqஹ⚪ᑖ᪆1.FᦟᩞP47ᑖ᪆yxḄᦪᡠᐜு=x=2y=6ᐭyxEᦪk,ᓽᑭᵨ~ᦪQᦪ᪆஺

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36Øᔲ"Â32+42Ú52ḄᐵÜ52+122D”2ḄᐵÜ,ᓽ32+42=52,52+122=132,ªᨵ_2+`2=Í2஺ßàḄ¬Jáᨵ./ឋâᔩäDr---------------7fÏஹå⚪ᑖ᪆\1(⊡ᐙ)éêÃᙠAABCëZC=90°,ᦪ@AB஺CḄDE9FGH᰿;Jᝰ஺L2MNᙠPABCQZC=90°,NAஹZB,NCḄSTbaabWUḄ.'TVWaL^\La|ᑣY4.'Ḅ☢[W஺\/^TS=4x"c2"\I7_TS=(a+b)2^TH_T☢[Wᓽ4X—ab+c2=(a+b)22ᓄ஺aஹbᚪde1.*+,ᳮḄᐹgᑁij_____________________________________________________2.᝞mnAABCḄopឋrjZC=90°,(ᵨuvwx⊤)পY┦nA}Ḅᐵ_____________________;AফDTQᑣTQஹব/B=30°,ᑣNBḄSTHT:ভTA}Ḅᐵ஺3.AABCḄTaஹbஹc,b2=a?+c2,ᑣ=90°b2>c2+a2,ᑣNBjnb2ீc2+a2,ᑣNBjApaBbC

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39Ç"5஺ভমÅOÈ%É0Ê6b⚪&'(ᙠaIbI"<%Ëf-2b஺D⚪&'(ÅOᐵ%Ì2É,'ÍÈÎÏḄᦪ'%ᵫIᓄḄᐵḄᓄ஺v2(⊡ᐙ)aIbI"ḄÓᑖÔ5O12,bc஺Aᑖ᪆<Õᜧ12V`aI%ÌV`Ã%cd3/\ᑖÙÚÛᑖÔÜ"஺&'(⍝ὃ⇋P⚪⌕ᐰ☢%ᑖA/\B஺/|\v3(⊡ᐙ)᝞/%ßAABCḄÓ`6cm஺••'RbAnপßAABCḄIW§஺ফSAABC஺ᑖ᪆ᳮḄ]ᵨ_`ᙠaIbI"<%cdef⌕g⌼aIbI"%YU`iᵨḄg⌼aIbI"ḄZ[\*஺âUCD,ãᐸåæçRt^ADCᡈRtaBDC<%èéᨵÅ%᪷ìßῪbI"b\ᔠÅឋî%AD=CD=^AB=3cm,ᑣd⚪ð஺2ñஹᚪo¢1.òó⚪পᙠRt^ABC,ZC=90°,a=8,b=15,ᑣc=஺ফᙠRtZXABC,ZB=90°,a=3,b=4,ᑣc=»বᙠRtZkABC,ZC=90°,c=10,ab=34,ᑣa=,b=஺ভÅôaIbI"ḄbbôõöᏔᦪ%ᑣøḄbÓᑖÔ஺মaIbI"ḄÓᑖÔ3cmO5cm,,ᑣbÓ஺যßbI"ḄÓ2cm,ᑣøḄU,☢ú஺A2.᝞/%ᙠaABC<%ZC=60°,AB=4A/3,7S.AC=4,AD`BCûḄU%BCḄÓ஺/3.ßῪbI"ῪÓ`10,üÓ`16,ýôßῪþ-------Ḅ☢஺ஹ1.⚪ᙠRt^ABC,ZC=90°,প᝞a=7,c=25,ᑣb=஺(2)᝞NA=30°,a=4,Ub=஺ব᝞NA=45°,a=3,ᑣc=஺ভ᝞c=10,a-b=2,ᑣb=஺ম᝞aஹbஹc᦮ᦪᑣa+b+c=__________o!(6)᝞b=8,a"c=3"5,ᑣc=_________஺/2.$%"᝞&'(ABCD)AD஻BC,AD±DC,/AB±AC,ZB=60°,CD=lcm,+BCḄ,஺/B0-ஹ.ὃ0ᫀ

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64ᨵ919.1.22Ḅᑨ——2ḄÒÉNஹᦟ+>᪗1.ᳮ2ÒÉḄᭆ#01{Ḅឋ.2.@-.ᙢXᵨ2ÒÉឋYᨵᐵḄ^_EÖ×.3.ØᔊqÚஹÛÜஹ^_ḄaK#YNÝÞß\ᳮ^Ḅ@k.4.@IᵨGᔠD^_ᨵᐵ2ÒÉឋḄ.ᳮᙠ^_aKᡠIᵨḄàáஹâஹãᓄv²ÜCD.ஹ'ஹå'1.'01EIᵨ2ÒÉḄឋ.2.å'2ÒÉឋḄ^_æçÉḄè~CD.3.å'ḄéẚCD1%ᦟᩞ2ÒÉḄᑁ)ᵫN⍝3⚪íîmᐸᭆEឋḄ#ðᦟᩞ½ὁᦟᩞᙠ$;!"Ḅòóôõ᣸·¤VḄ#{$Bõ᣸⌕÷øåL#§ᵫ¸+,ᙠù☢Ḅ+b#è~æçÉḄ.bûü#®ýòóôþÿ᣸Ḅឋ1⚪Ḅᜧᦟ⌕"ᑖ᪆Ḅ%&Ḅ'ὃ)*.,-.ᳮ01ᡠḄ345ᨵ78ᐵ:;ᨵᦪ=ᐵ:ὶ?@-)ḄABC᪀⌼78FGᑭᵨ78FGḄJG78KLMᩭ34ᡂPḄ'QRS&.2TUḄRḄVW11RḄXY1⚔RJGḄX.3⌕[ឋḄᱯஹᩩ_ஹ34`%ᵨabcd1ᱯ1ᙠfg⚪hiᨵjg34.g34⊤lᐵ:mg34⊤ᦪ=ᐵ:Yᩩ_⚪hn1XojGpᑮY341ᨵjgg⊤RrGḄlᐵ:mg⊤RrGḄᦪ=ᐵ:ᙠsᵨC᪷u◤⌕⌱ᵨᐸḄ34nY%ᵨ1ᙠ@AjGḄᩩ_iyḄ78ᐵ:`yḄzᑖᐵ:.4C{)⚪|}~,-.ᐸឋ.ஹ⚪Ḅᑖ᪆1ᦟᩞP98Ḅ4,ឋḄ⚪ᦟᩞᵨḄᐜᭆRឋḄS&⌕}~78FGḄឋRᑨᦟ

65ᙠᦟ-⌕[.1,Ḅᭆឋ|}~¡Ḅឋᯠ£2.2⍝⊡ᐙ⚪⌱§ὁᦟᩞḄg⚪ឋR78FGḄᑨḄ©ᔠsᵨ⚪⚪«¬ḄS&®¯34¡°±²ᵨᑮC᪷u-.³´〉¶Ḅ⌱2.ᦟ-⌕[ḄS&cdC¡·R¸¹ºᡈᦟᐹ.Fஹ½ᚪᐭ1.78FGḄឋY78FGḄᑨYÀÁᨵÂÃὶ:Ä2.ÅÆÇÇ78FGឋRᑨḄᵨ⌶ᔩÄÊ178FGABḄËᵨᒹÍgS☢1ÏoËᵨ78FGḄឋÐ0ÑÒÓÔ⚪.᝞ÖḄᦪyḄ×LMᡈyLMMYᑨgFG78FGØÙᑨÏ78MYᐜᑨgFG78FGᯠ£Ú£ᵨ78FGḄឋÐ0ÑÒÓÔ⚪.n3.Ûh³᛻ÝÞ1ßf-'ὃ1àágᑖᡂFgᐰMḄAÅ᝞ãᑗᒘḄÄÊᫀ᝞nᨵçg78FGÄÅ᝞ãᑨèḄÄBFCéஹ~⚪ᑖ᪆1ᦟᩞP984᝞DஹEஹᑖWAABCGABஹACḄAÖ1DE஻BCKDE=^BC.ᑖ᪆1ᡠḄ345ᨵ78ᐵ:;ᨵᦪ=ᐵ:ὶ?@-)ḄTyABC¡[⌕Ḅᑁìíᓄᑮg78FGᑭᵨ78FGBK________kḄJG78KLMḄឋᩭ34ᡂPØÙïÔ⚪pᑮ0Ñð◤⌕〉¶Ḅᩭ᪀⌼78FG.1S&11᝞1,ñ×DEòIJF,ïEF=DE,XoCF,/\ᵫ4ADEÀôCFE,CpAD஻FC,KAD=FC,ᨵBD஻D/_——A?---F7FC,BD=FC,ᡠ¡FGBCFD78FG.ᡠ¡DF஻/\/1J-------------0BC,DF=BC,DE=-DF,ᡠ¡DE஻BCKDE=—BC.õ22পC¡)C%CF஻ABaDEḄñ×÷FS&R☢ᜧºLfnS&21᝞2,ñ×DEᑮF,ïEF=DE,XoCFஹCDAF,;AE=EC,ᡠ¡FGADCF78FG.ᡠ¡AD஻FC,KAD=FC.AD=BD,ᡠ¡BD஻FC,KBD=FC.ᡠ¡FGADCF78FG.ᡠ¡DF஻BC,KDF=BC,DE=øDF,ᡠ¡DE஻BCKDE=ùBC.22ú1XojGḄyûḄ.

66ூ'ὃ௃11??1জgḄᐳᨵᩩঝḄᨵ2Ḅᨵ᪵Ḅᐵ1ḄᐳᨵᩩḄḄ⌕Ḅ!"#$.""Ḅ&'⚔")"Ḅ&.2ḄḄᐵḄ*+,-./Ḅ0.1Ḅឋ3Ḅ*+,-./Ḅ0.K45Uᑭᵨ89ᳮ,;<=>?ᙠAB᛻ᑖᒘ?ᩭḄGHᐰ.ᔩKLMNOᳮᵫ1Q2⊡ᐙ1TU᝞W1,ᙠGABCD,EஹFஹGஹHᑖABஹBCஹCD,DAḄ".Y=GEFGH*+G.ᑖ᪆[\TU"EஹFஹGஹHᑖḄ",]^পA_`ᵨឋ3aᑮGEFGHḄcdḄᐵ.ᵫ/GḄ)]^eGᑖᡂg,ᡠ^ijkl,&mACᡈBD,᪀⌼“”ḄstWu,v⚪x]y=.=>&zACW2,Z\DAG,'AH=HD,CG=GD,HG஻AC,HG=-ACឋ31.2$ᳮEF஻AC,EF=-AC.2Z.HG஻EF,-HG=EF.}GEFGH*+G.v⚪]yz~&zGGᩩḄ",ᡠyḄG*+G.ஹᚪ1.1᝞W,AஹBg"ᛢ◞,ᙠAB᜜⌱"C,&zACBC,ᑖa?ACBCḄ"MஹN,᝞yMN=20m,AஹBg"Ḅm,ᳮᵫ.2.TUḄᔜᑖ\8cmஹ10cm12cm,Y&zᔜ"ᡠᡂḄᕜ.3.᝞W,Z\ABC,DஹEஹFᑖABஹACஹBCḄ",11EF=5cm,ijAB=cm'BC=9cm,UDE=cm'2AFDEᨵᱯḄᐵ=>;Ḅ.ஹu1.1Ḅᕜ135cm,ᔜ⚔"¡)

67Ḅ*+,ᑣ8ᩩ*+ᡠ£ᡂḄḄᕜcm.2.1TU^ABC,"DஹEஹFᑖAABCḄ",᝞4DEFḄᕜ12cm,4ABCḄᕜcm.3.TU᝞W,EஹFஹGஹHᑖABஹBCஹCDஹDAḄ".Y=GEFGH*+G.19.2.1¤1ஹᦟL¦᪗1.¨©¤Ḅᭆ«ឋ3,ᳮ¬¤*+GḄὶ.2.®¯°±ᵨ¤Ḅᭆ«ឋ3ᩭ¬²ᨵᐵ³⚪.3.´µ±¶ὶஹ·¸¹ᑮ3¹Ḅº".}ஹ»"ஹ¼"1.»"¤Ḅឋ3.2.¼"¤Ḅឋ3Ḅᮣ¾`ᵨ.3.¼"Ḅ¿ẚÁ_1.¤ᙠ*+GḄÂÃÄ9ÅḄ.·9Å?Æ,✌ᐜ`ÉÊ9,¤*+G,ËÌᱯḄ*+GᱯcᜐÎᨵÏ.[vᙠᦟLᙠᡃÑÒᵨ±¶ÁÓÔÕ¤Ḅᭆ«Öឋ3,᝞ᵨ×ØÙᡈᦟᐹÛÜ,·*+Gᑮ¤ḄÛ¹Ý,yᑮ¤Ḅᭆ«,ᳮ¬¤*+GḄᐵ.2.ÞᦟLß⌕àLM>á1¤ᱯḄ*+G,2¤âã*+G×ᩩä”ᨵÏ“,#<ᵨ"GæÏḄ+G¤”ᩭ9Ť'3¤ᱯḄ*+G,ᐹᨵ*+GḄᑗឋ3ᐳឋ1,ßᐹᨵÌèéᱯḄឋ3ឋ1.3.·ஹஹ)Á☢]ëìÛÜᦟᐹ1,KLMºíᡈḄᱯឋ3.1)*+Gឋ3ï$,ðñïᚖÏឋ31.ó1'2GÏឋ31'3)ôï.-ñï*ᑖឋ32.4.õöLMᑭᵨ¤*+GḄ·÷ᐵஹ¤Ḅᭆ«^Öᐰ.ḄUø,ù=>gᩩឋ3Öû~.ᢣ?û~ýOþÏḄÿᑖᐵ⌕Ḅᩩឋᙠᡈᑖᐵ;ᵨᑮ.5."ABCDḄ#ᩩ$AC,BD%"ᑖᡂ'(ῪᓽAAOB,ABOC,+COD,ADOA.-./0123456ᙠ7ᩖ9:;<=ᑮ>⚪Ḅ@A.ஹC⚪ḄD9ᑖ᪆CIᦟᩞP104ḄC1,H"ឋḄIJᵨH◀Lᵨ5MNᡠ.Ḅ"ឋ᜜$QR⚪ḄSTUVLWYᵨ.C2ZC3[⊡ᐙḄ⚪^ᐸ:`aC2Ḅb>c-./L>de1fg"'[fh":ḄQRi⌕ᵨᑮḄឋjᑭᵨlmḄ@c>n:ḄQRopQR⚪:ᵨḄlqr2“tuvḄw”yz9ᑭᵨ☢|}T~ᑮ#uஹtutuvḄwḄyzᐵT.`aC2ஹC3Ḅb>./>nᨵᐵ"l☢ḄQR⚪^Z01⚪Ḅlq.

68'ஹᚪᐭ1.W/:'uḄ▭ᵨ9ᱏe⊟ஹ(ccd☢ᵨL'uḄ¡ឋ¢2.@ὃd¤Ḅ'uᦟᐹ¦¦§¨©ª«¬¡H'uᔩ¢g¡¢e¯°Wam᝞93.²³°W'uḄ´amµ´ᑮ¶·-./¨©¡9¢e¸..aḄl¹ᩈ⚪"»¼."»¼dᨵḄ'u½¾"e`U½l."ᡃÀᨬÂḄ9ÃC᝞ÄÅ☢ஹᦟÆÄḄÇ☢([ᨵ"È.ூÊË௃ᙠ'u᪾vᵨ#᪷ÏÐÑᑖÒᝅᙠÔ$Ḅ#⚔§veY¹$$ªÔÖḄ⚔§ᦋØ'uḄÙ.জÛḼNaḄØᓄ#ᩩ$ḄÞᑖÒ¬᪵ØᓄḄ¢ঝµNa'uØᡂ"hHḄᐸáᑁ¡᪵Ḅ¢HḄ#ᩩ$ḄÞᨵ¡ᐵ¢ãY@ὃஹäåஹæç2ᑮ"Ḅឋ."ឋ1"Ḅ'[."ឋ2"Ḅ$Ô(.᝞9ᙠ"ABCD:ACஹBDÔäè§0,ᨵAO=BO=CO=DO=-AC=-BD.fh~5ᑮḄ22ឋdtuvḄ:(ètuḄé.êஹCë⚪ᑖ᪆C1eᦟᩞP104C1ìíd᝞9"ABCDḄ#ᩩ$Ôäè§0,ZAOB=60°,AB=4cm,"$Ḅ.ᑖ᪆dfg"ᱯïḄ'uᡠ5Hᐹᨵ$Ô(ðñÔᑖḄᱯïឋ᪷ò"Ḅᱯឋ,ìí~aOAB(ufh$ḄÞ~.>d'uABCD"...ACZBDÔ(ðñÔᑖ.,OA=OB.óZAOB=60°,ôAOAB(u.

69"Ḅ$AC=BD=2OA=2x4=8ecm.2⊡ᐙ᝞ABCD,AB8cm,AD4cm.ADḄ!"AᑮBDḄ$%AEḄ.ᑖ᪆1*+,-./0*12Ḅ3456⌕ᵨᑮ09Ḅឋ;<1⚪ᑭᵨ?@ḄABCD092Ḅ34E/FG34⚪26ᵨḄ?H.ᶍCJAD=xcm,ᑣx+4cm,ᙠRtAABD2ᵫSTUᳮx2+82=x+42,CWx=6.YIIAD=6cm.2“09\]Ḅ^”/`-abᑭᵨ☢defgWᑮh0ஹ\!\]Ḅ^Ḅ`-abᐵkfAE*DB=ADxAB,CWAE=4.8cm.3⊡ᐙ᝞ABCD2E/BC]`"DFJ_AEqF,rAE=BC.sCE=EF.ᑖ᪆CEஹEFᑖtU/BC,AEvw]Ḅ`xᑖrAF=BE,ᑣy⚪CD

70ÆÇḄ+.(A)12cm(B)10cm(C)7.5cm(D)5cm2.ᙠ09ABC2ZC=90°,AB=2AC,NAஹZBḄ¬ᦪ.3.ABCD2BC=2AB,E/BCḄ2"sEA±ED.4.᝞ABCD2AB=2BC,AB=AE,sZCBEḄ¬ᦪ.19.2.1¦`ஹᦟÊË᪗1.ᳮCÍÎÏḄᑨU?H.2.ÑÊÒÓÔᵨU¢ஹᑨUvÕCDÖᓫḄsz⚪Ø34⚪Ù`ÚÛÜÊÒḄᑖ᪆ÓݦஹÞ"ஹß"1.Þ"ḄᑨU.2.ß"ḄᑨU!ឋ;ḄàᔠÔᵨ.3.ß"Ḅâẚ?H/ᨵ`-/0Ḅ·¸,ᙠᑨU`-,/ä/å✌ᐜèE-,/ä/·¸,éèêhḄᜳ/ä/0Eëᵨ“U¢”ᑨU/ᨬÞ⌕ØᨬabḄᑨU?HEíîïU¢ðᵨḄñÞឋஹឋ;ØᑨU.<ᐸêᑨU./“U¢”+aẠôõöᩭḄ.*1b⁚Â⌕ùúU¢±ûÍᢣöᵫ·¸,Wᑮ{◤⌕þÿᩩᯠὃ᝞HIḄ•!"ᩩ#$%&'(ᕖ*+,-.(ᑨ012.45ᑨ0121,⌕Ḽ:%&;ឋ=ᒹ?@ᩩAB1CDB2C@ᩩ4FGHI.45ᑨ02,J⌕Kᓽ#MNᵫᨵQFRF#$S.,ᵫ4FGHIᓾSU..NVWᓺYᡃ[\᣸V^1,ᙠᦟa#$〉cᙢefᑨgḄ⚪i.⌕j⍝B1C(Ḅᑨ012ᨵ$lQmAজFRFḄDঝ4FGHIḄDঞᨵQFRFḄ.B2C,ᵫ(qrḄ+sᐵuv(Ḅᑨ012w#ᑖN@y:জ+.{|}eQᱯ0ḄᩩDঝ+.{J◤eᱯ0Ḅᩩ.B3CᱯᙢAজ᝞ᡠḄᩩUQḄ0U(DঝᡠḄᩩQᩩᑨ012Uᑣ◤⌕ᑭᵨ0qᑨ012&ᡈ^l.ᙠᦟa◀ᦟᩞaᡠḄ᪾ᡈ(᜜#$ᔠ¡▭%&ᑨ0(Ḅ¡ᵨ£¤.Qஹ^⚪Ḅ¦§ᑖ᪆©⁚«ḄQ^⚪¬⊡ᐙ⚪^1ᙠḄ•¯ᑨg⚪NVWᳮ±ᑨ0(Ḅᩩ,ὁ³[ᙠᦟa#$〉cᙢefᑨgḄ⚪iD^2ᑭᵨ(j´µ¶·;^3⍝(Ḅᑨ0⚪Q⚪i+UḄF¹.{ᩭ»ᔠ¼ᵨ(0rᑨ0Ij´Ḅ.ஹ«ᚪ¾ᐭ1.!"À*!"À(*

712.(ᨵÂfឋ=*3.(ᨵ!"ᐳÄᜐ*ᨵ!"UÄᜐ*4.Æ^¾ᐭAÇ⌕(È᪾〈ᝤᝤËÌᱥ5Îᩭ@᪷йHIḄÑᩈᩩq@᪷йHIḄÐᩈᩩᑴÔÕᨵ!"Ö2#$×ØÙḄ(È᪾ᔩ*ÛÛÜḄ12#*ÝÞßᑮ(Ḅᑨ012.(ᑨ0121"4FáHIḄ(.(ᑨ0122"ᨵQFRFḄ(.Bᢣ.Aᑨ0(j⍝QFRFᩩãäV.MNᵫᑁFq#j;æçF0RF.Cèஹ^é⚪ᑖ᪆^1B⊡ᐙClᑡᔜìᑨ0(Ḅ%2ᔲîï*N!"*1ᨵFRFḄ(AX2ᨵFRFḄ(DW)B3F¬HIḄ(D3)B44FGHIḄ(D(x)54FGHIðñHᚖRḄ(DX64FGñHᑖðHIḄ(DN)74FGHIðᨵFRFḄ(DX8¯óᚖR•¯4ðHIḄ(;9@¯4ᑖð4FGHIḄ(.W)ᢣ.AB1CᡠḄᩩUQḄ0U(D2ᡠḄᩩQᩩᑨ012Uᑣ◤⌕ᑭᵨ0qᑨ012&ᡈ^l.^2B⊡ᐙCôjOABCDḄ4FGACஹBDHõ5ö0,÷A0BIQFAB=4cm,K;Ḅ☢ù.ᑖ᪆A✌ᐜ᪷üAAOBIQFr4FGñHᑖḄឋ=ᑨ0.ABCD(ᑭᵨýþ0ᳮ¶·Ð+,ßᑮ☢ù¤.±AAABCD**.A0=—AC,B0=—BD.22AO=BO,,AC=BD....ÿABCDḄ.ᙠRtZ\ABCAB=4cm,AC=2AO=8cm,BC=V82-42=473(cm).

72S^=AB*BC=4X4^=16^cm2.ABCI3⊡ᐙ᝞1,U7ABCDḄᑁḄᑖᑖ!"E,F,G,H.#$EFGH.ᑖ᪆⌕$EFGHᵫ!(⚪*+ᑖ,-./᝞2,0(+⌱ᵨ“45Ḅ”ᩭ$8.$8ABCD,AD//BC.B.ZDAB+ZABC=180°.:AEᑖ/DAB,BGᑖ/ABC,ZEAB+ZABG=-X180°=90°.2,ZAFB=90°.;ᳮ+$ZAED=ZBGC=ZCHD=90°.EFGHᨵ45Ḅ.>ஹ@ᚪBC1.⌱DEᑡGHIJḄ.AᨵKL5ḄKMBᨵKLN5ḄKMCOᑖḄDO⊡Ḅ2.᝞ᙠaABCZC=90°,CDPQRCDᑮ"E,TUDE=CD.VWAE,BE,ᑣACBEP.YஹZ[BC1.\]^Ꮭ`aᔠcd᪾ᑖE☢4ghi1ᐜk-lmᔠnoḄaᔠcdᧇ᝞জTAB=CD,EF=GHফ᤮tᡂ᝞ঝḄᑣwxd᪾Ḅy᪷{Ḅᦪ}⍝ᳮব5☠d᪾ḄK᝞ঞ᦮d᪾Ḅ᪾5Ḅlᩩ5d᪾◣x᝞টG8d᪾ᔠowxd᪾—᪷{Ḅᦪ}⍝ᳮ:2.ᙠRt^ABCZC=90°,AB=2AC,#NAஹ/BḄᦪ.19.2.2KKஹᦟ}*Ḅ:

731.ᭆ⍝Ḅᐵ.2.ᳮ,ḄMឋ1ஹ2ᵨwឋiᨵᐵḄ¡$¢£¤£¤Ḅ☢¥.3.¦§¨ᵨ©,ªᐹ¬⚪®¯ᑖ᪆°±¢²³°±.4.᪷{ஹḄ´µᐵ¦§¶ᔣ}¸¹º»ᔠ¼½.¾ஹ¿"ஹÀ"1.ᦟ}¿"Ḅឋ1ஹ2.2.ᦟ}À"Ḅឋ©ḄÁᔠÂᵨ.3.À"ḄÃẚÅH1ZᚪÆÇÈᵫᦋÊᡂ.T}¸ḄᐵᡂËÌḄᓺÎ2Ï,wMx⌕ᢕÑᭆḄ/ÂÃ-lᩩজÒঝKLN.Ó᜜Õ◤ᢣ-MØᑨM:ឋ.3Ḅឋ+ÚÛ}¸ÜÝᑭᵨᢚàஹáᑗḄÅHãäஹåæ.ÅHKKçRÅḄàèᢚéêᢚ᝞ᦟᩞP107Ḅãäᯠ[íḄîáEᡭðᓽàᱏÅH¾᝞1,lçóḄàᩩô¿õᙠKö¿õḄ÷ᑖABC஺ùv2ÅH4KçRÅàᢚéᙠᢚúÆûüýRPþáKῪᯠᡭᓽ᝞2.3⌕⍝ឋ1Ḅ᝞ABCD,AB=BC=CD=DA.ឋ2Ḅ᝞ᙠABCDACஹBD!"#$0,AC_LBD,AC%ᑖNBAD/BCD'BD%ᑖ/ABC/ADC.()ᮣ+,ᵨ.4ᢣ0123ᨵ5ᩩ2175ᩩ21Ḅᡠ95ᩩ21:!ᚖ<.5⍝ABCD=ACஹBDᑖᡂ?@AᐰCḄ<ᙠDEᡈGHIJᵨ7A.(6)Ḅ☢LMNS=2xS=2x(^xBDxAO)=BDxAO=^ab(ᐸaஹbMBD

74Ḅ5ᩩᑖRḄST.ᓽ“Ḅ☢LC#3Ḅ5ᩩSḄVḄWX”.Z⌕ᢣ0[\᧕^0SI_ᵨ%`@a☢LḄWbDEcdDE☢L5=eXf.ஹg⚪Ḅiᑖ᪆k⁚mn᣸?5Ag⚪g1W⍝⊡ᐙ⚪r?stḄឋ'g2ᦟᩞP108Ḅg2,7W⍝ᵨwx<wᩭ^☢LḄz▭|ᵨ}⚪.~⚪◀ᵨ9stឋ᜜,Z9ᵨ\ḄcdᩭDEḄ☢L9ஹᮣ+ᙢ,ᵨw.@ஹmᚪᐭ1.T%`@a%`@aḄᐵ2.ᐭTᡃ?WᱯḄ%`@a——ᐸzZᨵ¡᜜Ḅᱯ%`@a¢£¤¥¦§ᐜᢥ᝞ᡂḄ•«a9+¬Ḅᦟᐹ`¤¥T᝞®¯ᨵW«°a!CḄ%`@a.ூ²³௃1%`@a'2■•«°a!C.¶W·¸J+ᡠ¹ᑮ»ḄḄg¼.½ஹg⚪ᑖ᪆g1⊡ᐙT᝞@aABCDFAB¾W$,DF"AC#E.^GZAFD=ZCBE.GH'@aABCDCB=CD,CA%ᑖ/BCD.ZBCE=ZDCE.¿CE=CE,ABCE^ACOB(SAS).ZCBE=ZCDE.ᙠABCDAB஻CD,AZAFD=ZFDCZAFD=ZCBE.g2ᦟᩞPl08g2ᶍ

75ÂஹÃᚪ1.ÅḄaSC#WᩩḄSᑣ3ḄW«°ḄÇᦪᑖRr2.Ḅ5ᩩᑖR6cm8cm,^ḄᕜS☢L.3.ABCDḄᕜSr20cm,Õ!°5ᑁ×12,^ḄḄS☢L.4.I᝞ABCDEஹFᑖRCBஹCD¾Ḅ$ÕBE=DF.^GZAEF=ZAFE.Þஹm1.ABCDZDZA=31,ḄᕜSr8cm,^Ḅf.2.᝞@aABCDaSr13cmḄᐸBDS10cm,^1TACḄSÇ'2TABCDḄ☢L.19.2.2PAWஹᦟḄ1.ᳮà(áâḄ®¯ã5Aᑨ®cd'åᵨ7·ᑨ®cd`ᨵᐵḄGDE;2.ᙠḄᑨ®cdḄçèxéᔠ|ᵨëìḄíî)ïஹ¬ð)ïãñòóô)ï.õஹö$ஹ÷$1.ᦟö$Ḅ5Aᑨ®cd.2.ᦟ÷$ᑨ®cdḄGHcdã,ᵨ.3.÷$ḄøẚcdᐭI9ú»ᦟᩞP109ḄçýஹᦟᩞP109þ☢ḄÿᑭᵨᢚஹᑗḄᩭᐳḄᑨ!.ᙠᑨ!$%&'ᵨ(Ḅ“!*”ᑨ!&ᨬ-.ஹᨬ/⌕Ḅ1᜜3%ᑨ!4&5!*6-Ạ89ᩭḄ.:ᵨᑨ!1'.⌕<=ᐸឋ@ᒹB3%ᩩDEF1G&$%HIJKLF2G3ᩩNOPQRᚖT.6UVWᓺYZ[5DD^$_`abc᝞NOPQRᚖTḄJK&ᔩf6ghf'[ᵨr_Z<\\ᩭijkᯠNOPAC_LBD,s(t4u&.J3BCvᵨḄᑨ!6Fwxyᵫᦟ|}~GE

76(1)QR@STḄ>?@A(2)ᩩ@STḄ@AIn\PA(3)VWXYSᚖ[Ḅ>?@A(4)VWXYSᚖ[>ᑖḄ@A,<=EF2GF4GḄ⚪Z&JK•᪵(tḄ⚪ᩩD4ᒹᨵHIJKḄᑨ!ᩩD.᝞F4Gஹ᪷NOPQRHᑖ[5✌ᐜᑨ!JK&HIJK᪵ᑨ!F4Gᑨ!F3GU.ஹa⚪Ḅ=ᑖ᪆.⁚᣸U3%a⚪ᐸa1&ᦟᩞP109Ḅa3,a2&$⍝⊡ᐙḄ⚪¥3%⚪¥4&ᑨ!ḄT¦Ḅ§ᵨ¨⌕¥Ḅ&©ª«Ḅᑨ!¬ᵨ_ᑨ!IᨵᐵḄxi¯°._⚪¥Ḅ8ᳮ4²³´ᓫª«ᩭu¬ᨵgh¶·[5¸¹º»ᡂ.½¾¿$_ḄÀÁ[5⌱Ãa3.JஹᚪÅᐭ1.ÇÈF1GḄ!*EÉÊKRḄHIJKLF2GḄឋ@1ḄJᩩK4RLឋ@2ḄNOPQRHᑖËÌᩩNOPHᑖ$ÉNOLF3G§ᵨḄ!*IḄᑨ!:ᐹᜓ%ᩩDfFᑨ!E2%ᩩDG2.ூc⚪௃⌕ᑨ!$%JK&◀᪷!*ᑨ!᜜Òᨵᐸ(Ḅᑨ!ᔩf3.ூ௃FᦟᩞP109ḄGᵨ$Ó$Ô3᪷ᩈᩩᙠ(tḄÖᜐØ!$%|┑Úᡂ$%[ÛḄᓝÝJᕜßà$᪷áâãÚᡂ$%JK.Ûᩈᩩ%JKgh'᎛åᡂfæçèéê᧕ìᑮEᑨ!1NOPQRᚖTḄHIJK&.<=îᒹB3%ᩩDEF1G&$%HIJKLF2G3ᩩNOPQRᚖT.æçᦟᩞP109ï☢Ḅñ[5ìᑮ$òJKT¦ᑨ!ḄEᑨ!2JK4RḄJK&.óஹaÈ⚪ᑖ᪆a1FᦟᩞP109Ḅa3Gᶍa2F⊡ᐙGõöE᝞OABCDḄNOPACḄᚖTHᑖPKADஹBCᑖøùúEஹF.ýIÿAFCE./ABCD/\/X\/2AE஻FC.BC

77Z1=Z2.ZAOE=ZCOF,AO=CO,AAOE^ACOF.EO=FO.AFCE.EF1AC,/.CAFCEᚖḄ".#$3⌱&"'(᝞*+ABC,ZACB=90°,BEᑖ/ABC,CD_LAB.D,EH_LAB/H,CD0BE/F.CEHF1.ᶍ᧕CF஻EH,CE=EH,ᙠRtZ\BCE,ZCBE+ZCEB=90°,ᙠRtZ^BDF,,ZDBF+ZDFB=90°,61NCBE=NDBF,ZCFE=ZDFB,ᡠ8NCEB=/CFE,ᡠ8CE=CF.ᡠ8CF=CE=EH,CF஻EH,ᡠ8CEHF1.9ஹ;ᚪ=>1.?@1"ᑖḄ;2ᚖᑖḄB3CDᑖḄB4EFᑖGDḄ.2.HIJKLḄEᩩNᑖG16cmஹ8cm.3.᝞*OOABCDḄḄ0PDE஻AC,CE//BD,DEQCE0/E,OCED஺SஹTU=>1.VᑡᩩX,Yᑨ[Ḅ".AEᩩCBEᩩᚖCEᩩCDᚖDEᩩᚖᑖ2.'(᝞*MCῪ]ABC^BC_Ḅ,PDMLAB,EF1AB,ME1AC,DGXAC.MEND.3.`I`abIJᵫFᡂḄe*ᫀ.eḄN115cm,g14cm,hᨵIᩩᙠjIᩩ_ḄJFᡂkIJḄ0PUIJḄIJ⚔P.Hme*.

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79ᑨ^R6r-ᑨ^R6s▭)r᪷v^wᩭᑨ^.4Ḅឋᑨ^Wᜧ⁚!ḄஹஹḄឋOᑨ^Ḅᔠ.-{|W⁚ḄᦟD+,ஹ~☢ᡠDḄᑁY.A-{|W⁚ḄᦟDDEᙠḄ?ᭆ.Nஹ⚪ḄGᑖ᪆W⁚᣸N6⚪1ᦟᩞP1HḄ4,2O37⊡ᐙḄ⚪.ᐸ1O2ឋḄᵨᙠ!FGDElḄᵨᐸឋ.3ᑨ^Ḅᵨᐜᑨ^•6p?@¡¢£-ᑨ^R6.¤¥-p¦?@ᑨ§⚪*¨&©ª«¬¤ᚪ¨&1,¯°DEḄ±²-.ᑨ§⚪ᦋ´ᑡ¶⚪CDE±ὃ0জ15923Ḅᔩº»¼ºঝ159:2ᚖ8Ḅᔩº»¼ºঞ159ᚖ8¿23Ḅᔩº»¼º᝞ÀÁÂ)»¼ᩩúটlÅ“ᩩ723Ḅ”ᔩº»¼ºঠÅ“6523Ḅ“1ᔩºஹᚪᐭ1.¦?¦0ᵨ?ÊËḄÌᱏ«᝞ᡠÎÏᢚÑ?6.ஹ---------DEᙠÓÔ¦1ÕEÖឋ×ØÙÖÚOḄ|ᐵÜ.¶⚪0»¼᪵ḄºIݦ.ᢣÑ0ᙠR6ᜧß´^wḄᐸ^wᒹáK_G01ᨵ?@¡23Ḅ«Ï?►2ᨵ?6585Ḅ«Ï?►/2.ூ¶⚪௃ᨵ»¼ឋºᵫḄ^w-æÚçᨵ?@¡23Ḅᨵ?6585Ḅ.ᡠᐹᨵḄឋèᐹᨵḄឋ.

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81ABCDZBAD=ZADC=90°,AB=AD=DC«Ḅᩩ72365785Ï.Zl+Z2=90°.Z3+Z2=90°,Z1=Z3.AABM^ADAN.AM=DN.èᳮAN=DP.AM+AN=DN+DPᓽMN=PN....PQMN«ᨵ?@¡23ḄÏ.ûஹ¤ᚪ¨&1.Ḅᩩ,65,Kᩩ1592.´ᑡÅøᔲÙÅᳮᵫ.জ15923Ḅ4«Ïঝ159:2ᚖ8Ḅ4«Ïঞ159ᚖ8¿23Ḅ4«Ïটᩩ723Ḅ4«Ïঠ6523Ḅ.«Ï3.ëÚ0᝞ABCDEஹFᑖôCDஹCBþË9)Ḅí¿DE=BF.ê0NAFE=NAEF.4.᝞EABCDᑁ?í¿aEBC3N5ê/EADONECDḄÿᦪ.ஹ1.᝞EABCDḄCDFCBḄDE=BF.EA±AF.2.᝞4ABCZC=90°,CDᑖNACB,DE±BCE,DFLACF.!CFDE.

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