2021-2022学年福建省厦门七年级（下）期末数学试卷（附答案详解）

《2021-2022学年福建省厦门七年级（下）期末数学试卷（附答案详解）》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

2021-2022
ḕ᜜᪥ᑖ᪥
ᦪᔁ1.ᑡᦪᳮᦪḄA.-
B.|-2|C.V2D.V82.ᑡᔜ+,-ᡂ/0123ḄA.I,I,2B.2,3,4C.I,3,53.᝞:;<=>Ḅ?Ḅᙶ᪗B,A.3,-4B.3,4C.—3,—4D.-3,44.ᑡFGᐸ〉ᔠKᵨM᪵FGḄA.FGOP50RSḄTUVWB.XYZ[\]^_`S4RS-CoV-2cd_eS/fghijḄᏉlVWC.Xmn“pq9s”ᡂuvwxᐸyz{|}~GD.~Ḅ5.᝞:ᡠᑡᩩ{,AB஻CEᡂḄᩩ{AA.Z.A=4ACEABXAZB.NB=ECDC.B=AACED.4B+BCE=180°6.ᑡ0⚪Ꮇ⚪ᨵজᑁ┯2}¡ঝ£-3%>-3y,ᑣx>y¡ঞ123Ḅ/0᜜2ᜧ«¬/0®¯°Ḅᑁ2¡ট£a<—1,´µJ,a2>1.A.10B.20C.30D.407.¸2x<6-%ḄZ¹A.%<2B.x<2C.x>2D.x>28./0º»¼3Ḅ/0᜜260஺ᑣ¾º»¼3Ḅᑁ2¿)A.720°B.900°C.1085°D.1260°

19.ÁÂÃXÄÅÂÆÇÈÉÊᵨᐹÌᓫÎᕡឋÑÒÓᜧÔÕ᰿ᐸ“×ØÙØᵪ;ᓨ/ÜÝÞ……”Ḅàáâãä»eåæ.᝞:/çÁÂḄ/zᑖᙠÁÂÂçé☢2ᙶ᪗ëÁÂ;ºì3Ḅ¼íTX/0ᓫîíהḄᙶ᪗(4,a),“”Ḅᙶ᪗X(ñ3),ᑣ“ò”Ḅᙶ᪗X()A.(-3,1)D.(1,-3)10.᝞:ó04BḄ¼08ᙠxôḄºõôé?8Ḅᙶ᪗X(3,0),öAOAB÷xôᔣùú20ᓫîíïûᑮACDE,ýþAC,DB,£ADBEḄ☢ÿ3,ᑣA.-B.1C.2D.-2211.Ḅᦪ.12.ᙠ᪵60ᦪᑖᙠ5ᑁஹஹஹᦪḄᦪᑖ4,16,17,5,ᑣḄ⚣ᦪ.13.xஹy!"#ᑣx—yḄ$.14.%&CZ)ᵫ%&AB()*ᑮḄ,41,3)Ḅ./,,C(—3,5),ᑣ,B(l,6)Ḅ./,DḄᙶ᪗.15.ᡃ3ᦪ45678ᙠ9:3;<⌶>ᑮ?@ABCḄDE▅GḄᩖIAᨵ⍝LM⚪OP59319ḄQ"᪷678ῃTU:Vᫀ39,BCḄDEX

216.᝞ᙠABCB஺ஹBEᑖ4BCḄ%(ᑖ%,ᙠC4Ḅ%AFHBE
BDஹG,
BCஹH.ᑏ:NFGD,48E,4cḄḄᦪᐵO.17.(1)YZO2-3+g+|l-2|(2)"#Or°(஺TL>y—JL18.(1)⌕ᦪ^1Ḅ$¡ᦪPxḄ¢$¤;<5%—1>3(%+1)(2)¥¦13§ᙠᦪ¨A⊤ª«.l-x—is/—X<2219.᝞AC//FE,N1+43=180°.P¬O/.FAB=Z4.20.ᦟ®¯]°Ḅ±ᐵ²³´µ¶·4¸ṑḨ»ᳮ½¾Ḅ¿À⌕PÁ¸ÂᜩṑḨÄ/Åᑮ9·Ä.Æ4¸ÂᜩḄṑḨÄ4᪥È@ÉÊƯᑖ4¸Ë4¸ṑḨÄᑖA,B,C,஺(ÂÌ4¸ÍÎ⌱ÐÑÒÓ⌱ÐÔÕÖ)OAOṑḨÄ<8·ÄqHO8·ÄSṑḨÄ<9·ÄqCO9·ÄWṑḨÄ<10·Äq஺OṑḨÄ210·Äq᝞12᪷ÉÊÚtÛᑴḄ¥e᦮ḄÝYb᪷ÞßḄàáV]ᑡ<⚪O(1)ãÉÊḄ4¸ᨵq(2)⊡ᐰᩩæÝYq(3)bçYᐰ᪥800Ì4¸ṑḨÄ¥!9·ÄḄᦪ.

321.᝞ᙠ(☢êᙶ᪗æABCḄ⚔,ᑖ4(-1,6),8(-4,3),C(l,4).ËæABCᐜᔣö()4ᓫmøᔣ]()3ᓫm*ᑮæ4B'C'.(1)bᙠú:()wḄæAB'C'q(2)æ4B'C'Ḅ☢û.22.“ýþþ”“”ᑖᓅ2022ᝍᝍḄᔡἝᱥ.2019ᐵᱯ"ᖪ$ᢗ&'(ᢝ*+├.-ᝍ./ᱯ"ᖪ$0123456ᢇ869:Ḅ“;<<”“”=ᐹ?*@AᨴḄ├1CD᝞⊤G├1`/|}ᨴz├1~/|ᐗ;<<1Aᨴ639902Aᨴ851410(1)JKL“;<<”“”=ᐹḄ01MNO(2)-ᓫQR3ST@L=ᐹUVᝍWXYZ[\Ḅᝄ$⌕J“”Ḅᦪ`ាbcd“;<<”Ḅᦪ`Ḅ2ef3Sghijklm9000ᐗ.o᪷q⌕Jrs3S/ᫀuk“”3Svᑮᨬᜧᦪ`.4⚓ᐳ18⚓

423.WᐵdxyḄ/:;0,fa<3.(1)஺=2,J/Ḅ.(2)/Ḅjcx-y>m,fᔠ⌕JḄ᦮ᦪaᨵ@AJ஻?Ḅ.24.(1)᝞1,ᙠ4BC¡44cB=90°,NE=35°,COAB¢£Ḅ¤¥4BCḄ᜜§NBAGḄ¨ᑖ©ª«©C஺d¬F,®FABCªd¬E.J"Ḅ°ᦪ.(2)᝞2,ANAABCḄ᜜§NB4GḄ¨ᑖ©®8c24ªd¬M,¬஺ᙠ¢AB£f±4CD=4B,NB4CḄ¨ᑖ©AEªCCd¬F.²³´NMµNCFEḄᦪ`ᐵ¶·¸¹º».25.¼©᜜6¬ᑮTᩩ¼©Ḅ¾¿jᜧd1,ᑣÁTA¬¼©Ḅ“ÃĬ”.ᙠ¨☢¼§ᙶ᪗¶¡W>1(1,a),B(2a,b),C(-i,b+l),m¬MU¼©k¨ÈdyÉÊAABC¨ËVAOEF,¨Ë¬A,B,CᑖÌͬ஺E,F.প¬A(Ïᑏ“”ᡈ“j”)¼©ᓃḄ“ÃĬ”O(2)¬ÓÔbÕᙠ¼©"£¬EÕᙠ)É£fÖᙶ᪗V2a-b,OOEḄ☢×V4,m¬AU¼©"¨Èdxɬ8ᔲV¼©LḄ“ÃĬ”Ù»ᳮᵫ.26.᝞W¼©/µ¼©MMP஺ᑖªd¬AஹB,C!"#MN&',PO£/ABÝÞḄ6¬41+42=180஺.12(1)JºGMN//PO*(2)AC,BCᑖ¨ᑖZB4N,^ABQ,oᙠ1¡ßà¬C,·?ÄAC,BC.ᑨáACµBCᔲᚖ¼·Ù»ᳮᵫ(j⌕JãäU)O(3)᝞2,mA¬UAEᚖ¼d¼©PQ,ªÓQd¬E,¬஺«©AN£6¬?ÄCD,CE,ZC=90°,U±4DCḄ§¨ᑖ©OF,ªCEd¬å¬஻Ḅ

5æ⊡§¨ᑖ©£6¬?ÄHFNCFH-±4DF=90஺²ᑨá«©E"£ᔲðᙠ6¬åᨵDF+HF>OR,Ù»ᳮᵫ.6⚓ᐳ18⚓

6öᫀ᪆1.ூöᫀ௃Cூ᪆௃Gᑖᦪúdᨵᳮᦪᦑü⌱⚗jᔠ⚪
B.\-2\=2,᦮ᦪᨵᳮᦪᦑ⌱⚗ᔠ⚪
C.ᡃᳮᦪᦑ⌱⚗ᔠ⚪
D=2,᦮ᦪᨵᳮᦪᦑ⌱⚗ᔠ⚪.ᦑ⌱C.᪷ᳮᦪ▲ᦪᫀ.!⚪"⌕ὃ%&ᳮᦪḄ()*+᪷,Ḅ⌕-./0ᳮᦪ▲ᦪ1ᳮᦪ.᝞ᐔV2,0.8080080008…(567889:;<170)=>?.2.ூᫀ௃BூC᪆௃CAஹ•••1+1=2,F11,1,2ḄGᩩIJKLᡂGN>⌱⚗ᔠ⚪
Bஹ,03—2<4<3+2,F12,3,4ḄGᩩIJKLᡂGN>⌱⚗ᔠ⚪
Cஹ•/•1+3=5,F11,3,5ḄGᩩIJKLᡂGN>⌱⚗ᔠ⚪
3+5V9,OF13,5,9ḄGᩩIJKLᡂGN>⌱⚗ᔠ⚪
ᦑ⌱B.᪷GN>ḄGPᐵRᑨTᓽ.⚪ὃ%ḄGN>ḄGPᐵRVWGN>6P8XᜧZGPஹGN>Ḅ6P[ZGPC⚪Ḅᐵ\.3.ூᫀ௃DூC᪆௃Cᵫ^_`abḄcᙠZOe▲f7⌱⚗ghᨵ(-3,4)ᙠZOe▲.ᦑ⌱D.ᐜᑨTj`abḄcᙠZOe▲k᪷ᔜe▲ᑁcḄᙶ᪗ᱯqC.⚪ὃ%&ᔜe▲ᑁcḄᙶ᪗Ḅ,ᱯqWbᔜe▲ᑁcḄᙶ᪗Ḅ,CrḄᐵ\,f7e▲Ḅ,ᱯcᑖuZve▲(+,+);ZOe▲(-,+);ZGe▲(v,v)
Zfe▲4.ூᫀ௃D

7ூC᪆௃C4{%|}50~Ḅ〉ᔠᵨᐰ☢{%/?ᦑ⌱⚗ᔠ⚪
A1&C(S4RS-CoV-2)vḄᏉ〉ᔠᵨᐰ☢{%/?ᦑ⌱⚗ᔠ⚪
C.1“9,”ᡂ¡¢£ᐸ¥¦§¨©ª%〉ᔠᵨᐰ☢{%/?ᦑ⌱⚗ᔠ⚪
Dª«g¬Ḅ®¯°±〉ᔠᵨ²᪵{%/?ᦑ⌱⚗ᔠ⚪
ᦑ⌱D.ᵫ´%ᑮḄ{%¶·¸¹º»ᡠ½ஹᱥX¿9¹<À²᪵{%ᑮḄ{%¶·¸¹ÁÂ.⚪ὃ%&²᪵{%Xᐰ☢{%ḄÃu⌱Ä´%Ų᪵{%⌕᪷ᡠ⌕ὃ%Ḅ£eḄᱯqᮣÇ⌱ᵨvÈᩭÊ£ᐹᨵẚÍឋḄ{%ஹϨ©´%ஹ´%Ḅ)ᡈÑÒᜧÓ⌱IJ᪵{%£ÔÕ⌕Ö×Ḅ{%ØᐵÙᜧḄ{%ÚÚ⌱ᵨ´%ØᐵÙᜧḄ{%ÚÚ⌱ᵨ´%.5.ூᫀ௃CூC᪆௃CAஹ•••/.A=Z.ACE,.■.AB//CE,ᦑ⌱⚗ᔠ⚪
Bஹ,0NB=4ECD,•3AB//CE,ᦑ⌱⚗ᔠ⚪
Cஹ••Z-B=Z-ACE,/•/ABÛCEḄᐵRÏ(ᦑ⌱⚗ᔠ⚪
Dஹ•:B+BCE=180°,AB//CE,ᦑ⌱⚗ᔠ⚪
ᦑ⌱C.᪷Ü©IḄᑨ((ᳮ£ᔜ⌱⚗¨©⌲vᑨTᓽ.⚪ὃ%ḄÜ©IḄᑨ(V_Ü©IḄᑨ((ᳮC!⚪Ḅᐵ\.6.ூᫀ௃AூC᪆௃Cজᑁ┯Nà=6áIÜ©âãä⚪ᔠ⚪
ঝæ—3x>-3y,èτéḄv7᜜Nᜧïðv7Û8àñḄᑁNâãä⚪ᔠ⚪
টæa<—1,ᑣa2>1,âãä⚪ᔠ⚪.Ꮇä⚪ᨵ17ᦑ⌱A.ᑭᵨÜ©IḄឋ°ஹ=?Ḅឋ°ஹGN>Ḅ᜜NḄឋ°=_õᑖuᑨTöᓽ(âḄ⌱⚗.Z8⚓ᐳ18⚓

8ὃ%&ä⚪Û(ᳮḄ_õC⚪Ḅᐵ\&CÜ©IḄឋ°ஹ=?Ḅឋ°ஹGN>Ḅ᜜NḄឋ°=_õùÕᜧ.7.ூᫀ௃AூC᪆௃C2xW6-x,ú⚗2x+xW6,ᔠûü⚗3K<6,Rᦪᓄ11,x<2,ᦑ⌱A.ᑭᵨ=?Ḅþឋ°ú⚗ஹᔠûü⚗ஹRᦪᓄ11.⚪ὃ%&Cÿᓫ
Ḅ
⌕
Ḅឋᙠ
Ḅᡈᦪᡈ᦮
Ḅᔣ
!"ᙠ
Ḅ#$ᡈ◀$&ᦪ
Ḅᔣ
!"ᙠ
Ḅ#$ᡈ◀$'ᦪ
Ḅᔣᦋ!.8.ூᫀ௃Aூ᪆௃ூᑖ᪆௃⚪ὃ,-.Ḅᑁ012᜜014ᳮ6⚪Ḅᐵ89:;<&-.Ḅᦪ2=>-.Ḅᑁ01?.᪷-.Ḅ᜜0Aᦪ1-.᜜01B:;<&-.ḄᦪCᵫ-.Ḅᑁ01?:;ᐸᑁ01.ூ௃F<&-.ḄᦪGF360஺+60஺=6,<&-.Ḅᑁ01G:(6-2)x180°=720°.ᦑ⌱FA.9.ூᫀ௃Aூ᪆௃Fᵫ“P”ḄRᙶ᪗94,“U”ḄVᙶ᪗G3,B:W

9lm.10.ூ6ᫀ௃4ூ᪆௃F4(m,n),VB(3,0),:.OB=3,ᵫXḄឋBOC=BE=2,
BC=OB-OC=1,,**S&DBE=]X2X?1=3••n=2,'•S"C8=-xlx3=-,ᦑ⌱FA.m,n),ᑭᵨ0.☢?:;஻ḄC:;BC,BWi.⚪ὃ,ᙶ᪗2_.!ᓄ-X0.Ḅ☢⚪Ḅᐵ89:;]AḄVᙶ᪗.11.ூ6ᫀ௃V5ூ᪆௃F¢ḄU£ᦪ9¢ᦑ6ᫀGFV5.᪷¤ᨵ¦
Ḅᦪ§GU£ᦪBW6ᫀ.⚪ὃ,k¨ᦪḄឋᙠᦪḄ©☢'ª9«ᦪḄU£ᦪ.12.ூ6ᫀ௃18ூ᪆௃Fᵫ⚪eWF60-(4+16+17+5)=60-42=18,/•.¯°±Ḅ⚣ᦪ918,ᦑ6ᫀGF18.᪷³´ᦪ¯ஹµஹஹ¶±⚣ᦪ1·¸¹ºᓽB6.⚪ὃ,k⚣ᦪ2⚣᳛=¼½¾⚣ᦪḄe¿9⚪Ḅᐵ8.13.ூ6ᫀ௃1ூ᪆௃FᙠÀ±ÁÂᓃFF`(XᓝLy——জ-ঝWFx-y=1.ᦑ6ᫀGF1.¯10⚓ᐳ18⚓

10ÉÊ9:WÀ±ḄËX,yḄÍᐭᑮÍᦪ:ÐqrÀ±ÑᦪḄ[ᦪᱯ]ËÀᑖÔÕÖ᦮×ZØUᓽB:Wx-yḄ.h⚪ὃ,µᐗ´À±Úeh⚪ḄÛÜÊ.14.ூ6ᫀ௃(1,8)ூ᪆௃F]4(-1,3)ḄÝ{]GC(-3,5),BRᙶ᪗ᵫ-1!G-3,ᔣÞßk2ᓫàVᙶ᪗ᵫ3!G5,⊤âᔣßk2ᓫàã98(1,6)ḄÝ{]DḄRᙶ᪗G12=-1,]஺ḄVᙶ᪗G6+2=8,ᦑ஺(-1,8).ᦑ6ᫀGF(L8).᪷]4(-1,3)ḄÝ{]GC(-3,5),BRᙶ᪗ᵫ-1!G-3,ᔣÞßk2ᓫàVᙶ᪗ᵫ3!G5,⊤âᔣßk2ᓫà$hlmBW஺ḄÝ{]Ḅᙶ᪗.h⚪ὃ,kᙶ᪗2_.Ḅ!ᓄ-X᪷4(-2,3)!GC(-3,5)Ḅlmå]Ḅ!ᓄæᓄGᙶ᪗Ḅ!ᓄ9⚪Ḅᐵ8.15.ூ6ᫀ௃347ூ᪆௃F(1)᝞jᑜ59319é☢Ḅà319Wᑮᦪ59,ê33=27,43=64,B$f4ëìíḄᓝàḄᦪ93,ᵫh:W὜ïḘ=39.ᦑ6ᫀGF3"(2)103=1000,1003=1000000,ê1000<103823<1000000,A10

11•Z.AEB=Z.ABE4-C,vBD1FC,FH1BE,••Z-FGD=Z-AEB,•Z-FGD=Z-ABE4-ZC,ᦑᫀ1/-FGD=/.ABE+ZC.᪷4&'ᑖ)Ḅ5678&9᜜&Ḅឋ<=>?@AB.C⚪ὃEḄ8&9ᑁ&75ᳮABGᵨ8&9ḄIஹ&'ᑖ)ḄᭆLMN8&9᜜&Ḅឋ<⚪ḄᐵP.17.ூᫀ௃R1STU=2XY3ᡈY2+\Y1=-3]ফ_`᦮ᳮbcdefঝ■জb2x=-2,bx=-1,jk=—1mᐭজb-1+2y=3,by=2,ᑣ_`Ḅ1qz21ூ᪆௃R1STUᑭᵨt᪷56MNuvwḄmᦪx6ᓄz{|ᓽ~w]R2S_`᦮ᳮᑭᵨᐗᓽ~.⚪ὃEeᐗY_`ᑭᵨᐗḄᐗḄᨵmᐭᐗᐗ.18.ூᫀ௃(1)ᵫ⚪xb:322(2%—1)—3(5%+1)—6N0,4%—2—15%—3—6N0,4%—15%2+3+6,-11%>11,X<-1]5x-l>3Rx+lS@R2S1_147-"ঝ’Uজbx>2,Uঝb%<4,.••TU`Ḅ¡12

12¦U`Ḅ¡ᙠᦪ¨©⊤«᝞ᡠ«:-5-4-3-2-1012345ூ᪆௃11᪷4⚪x~b-Y120,ᯠᢥ᯿YᐗYUḄ²³,´µ{|ᓽ~.
2ᢥ᯿YᐗYU`Ḅ²³´µ{|ᓽ~.C⚪ὃEYᐗYU`YᐗYUᙠᦪ¨©⊤«UḄ¡mᦪUw¶B·¸ᙢ´µ{|⚪ḄᐵP.19.ூᫀ௃=>••/AC஻EF,Z1+Z2=180",º//•Z14-Z3=180°,/•/z.2=Z.3,FA//CD,:.Z-FAB=Z.4.ூ᪆௃ᵫ»~=b42=N3,᪷4'µ)Ḅᑨ5bᑮ᪷4'µ)Ḅឋ<ᓽ~bᑮN/MB=Z4.C⚪ὃE'µ)Ḅᑨ57ឋ<·¸¾ᵨᑨ55ᳮ7ឋ<5ᳮ⚪ḄᐵP'µ)Ḅឋ<¿À)'µÁÂ&Ã]¿À)'µÁÄᑁ&Å⊡]¿À)'µᑁ┯&Ã.'µ)Ḅᑨ5ᵫ&ḄᦪÈᐵÉᑨÊ¿À)ḄÂËᐵÉ.'µ)Ḅឋ<ᵫ'µᐵÉᩭÍÎ&ḄᦪÈᐵÉ.¾ᵨ'µ)Ḅᑨ57ឋ<5ᳮÏY5⌕ÑÒ⚪Ó7?@,ᑗÕÖ×.20.ூᫀ௃200ூ᪆௃11CᐳØE90+45%=200
ÙSᦑᫀ1200
2B`ÚÛᨵ200-20-90-30=60
ÙS⊡ᐰḄᩩ9Þ{᝞2ᡠ«别

13(3)800xß=320(Ù)à{¦᪥ÚÛ'ᙳãᜩṑḨÏçè9hḄᨵ320Ù.(1)᪷4C`ḄÙᦪ7ᡠᓰḄêᑖë~M{|CᐳØEìíîÚÛ](2)᪷4(1)ïḄ?ð~M{|B`ḄÙᦪᯠᓽ~⊡ᐰᩩ9Þ{](3)᪷4Þ{ïḄᦪ4~M{|¦᪥ÚÛ'ᙳãᜩṑḨÏçè9/2ḄÙᦪ.C⚪ὃEᩩ9Þ{ஹᡧ9Þ{ஹᵨ᪵Cà{óôC⚪ḄᐵP>B⚪xᑭᵨᦪ9?ᔠḄ.21.ூᫀ௃6ூ᪆௃(1)᝞8&9AB'C'1ᡠ.(2)8&94B'C'Ḅ☢÷3x5-gx3x3-ix2x2-ixlx5=6.22ᦑᫀ16.(1)Àøᑭᵨ'ùḄឋ⚪?:AB:C$:g*Jo°*-“/00”2ᐹḄ56789120ᐗ“;<=”2ᐹḄ5678990ᐗ.(2),DE“/00”mF,ᑣDE“;<=”2஻?F>⚪?*120nl+90x2mW9000,$*m<30,K••/m9᦮ᦪ•1•niḄᨬᜧQ930,•••27nḄᨬᜧQ960.RD“/00”30F“;<=”60F.ூ$᪆௃(1),-“/00”2ᐹḄ56789xᐗ“;<=”2ᐹḄ56789yᐗᑭᵨ├6WX=├6ᓫ7x├6ᦪ[ᓽ]ᐵ^x,yḄRᐗ_`abc$de14⚓ᐳ18⚓

14ᓽ]hij2
,DE“/00”kFᑣDE“;<=”2kFᑭᵨW7=ᓫ7xᦪ[hᔠW7mno9000ᐗᓽ]ᐵ^஻Ḅ_ᐗ_`mpq$dᓽ]rḄsQuvhᔠm9᦮ᦪᓽ]hi.w⚪ὃRᐗ_`abcḄᵨ_ᐗ_`mpqḄᵨ$⚪Ḅᐵ&#*x1
yzp[ᐵ{ᑡRᐗ_`abcjx2
᪷~ᔜᦪ[dḄᐵ{ᑡ_ᐗ_`mpq.23.ூᫀ௃$*x1
a=2,ᑣabc9+=2®,x—5y=6{2জ-ঝ:8y=-4,$*y-y=-,ᐭজ*x-|=2,$=%_abcḄ$921j[y=-22
abᑮ2x-2y=4+2a,ᓽx-y=2+a,x—y>m,2+a>m,a>m—2,///Q<3,ᔠ⌕Ḅ᦮ᦪ஺ᨵA0

15(2)zM+^CFE=90°,¢£*///CஹAஹGᐳ4£ஹAN9
ᑖ•EAN=90°,K//•GAN=4cAM,•+CEF=90°,vCEF=Z-EAB+B,Z.CFE=Z-EAC+ACD,Z-ACD=B,:.Z-CEF=(CFE,Z.M+Z.CFE=90°.ூ$᪆௃(1)ᵫ¥

Ḅឋ§⚔
Ḅឋ§]4G4F=55஺ᑭᵨ
ᑖḄ©ª]NZMF=55஺v᪷~¥

Ḅឋ§]$j(2)᧕NE4N=90஺]NM+NCEF=90஺vhᔠ
᜜
Ḅឋ§]CEF=LCFE,]NM+4CFE=90°.w⚪ὃḄ#
Ḅ᜜
Ḅឋ§ஹ
ᑁ
®©ᳮ°±
Ḅ_᜜
p^®²m³Ḅᑁ
Ḅ®#$⚪Ḅᐵ&.25.ூᫀ௃#ூ$᪆௃$*(I”.•Aᑮ¥kḄ´µ=*¶1,/••4#¥kḄ''¸¹”.ᦑᫀ9*#.(2)•.•»¼½¾ᙠ¥kC(-|,b+l),.•.4BCᔣÁḄ´µ91:.2஺=—1,:.Q=ߟߟ,2.•/஺ḄÂᙶ᪗92,•••ODEḄ☢94,*,.~x|-1—b|x2=4,b=-5ᡈ3,Æ஺=_Çb=-5È71(1,-1),5(-1,-5),ÈBm#¥%Ḅ“¸¹”.Æa=-[,b=3È4(1,_8(-1,3),ÈBm#¥LḄ“¸¹”.ÊᡠÌBm#¥LḄ“¸¹”.(1)᪷~“¸¹”Ḅ©ª$ᓽ]j(2)ᑭᵨᣚḄឋ§ᑖÍa,6ḄQ]hi.w⚪ὃᙶ᪗ÎÏᓄ-
Ḅ☢“¸¹”Ḅ©ªpÑÒ$⚪Ḅᐵe16⚓ᐳ18⚓

16&#ᳮ$⚪?ᮣÔÕᵨᡠÖÑÒ$×Ø⚪.Ï1,:z.1=z.3,Z.2=44,z.1+z2=180°,//.43+44=180°,•MN//PQ(2)$*hi*AC1BC.ᳮᵫ*᝞Ï1_1Ú••/N4B+4QB4=180஺-AC,BCᑖÍᑖZN4C,Z.QBA,•••ACAB=-NAB,/.CBA=-/.QBA,22”•••/LCAB+ACBA=i(4NAB+“BA)=90°,ZC=90°,AC1CB-,(3)$*Ûᙠ.ᳮᵫ*᝞Ï2ÚܹDE.ÝÞ஺»ßPQ^J,,"/ßPQ^K.

17••MN//PQ,Z-ADF=FJQ,vCFH=FJQ+FKJ,CFH-Z.ADH=90°,♦FKJ=90°,ᓽFH1QP,vAE1PQ,:.AE//FH,A^LHEW=EHF,//•»”ᑖ4CEW,HEF=Z.HEW,♦FEH=FHE,:.FE=FH,••FE+FD>DE,FH+DF>DE,E9ᙊâE£>9ãäåæßEH^çÈDF+FH>ER,•••èEHÛᙠ_R,éDF+HF>DR.ூ$᪆௃(1)ᑭᵨêëᑁ
ì⊡¥ᓽ]j(2)hi*AC1BC.¢£4a4B+“BA=90஺ᓽ]j(3)Ûᙠ.¢£FH=FE,ᑭᵨDF+EF>DE,]hi.w⚪ï^ðñᣚÊᔠ⚪ὃîḄᑨ©®ឋ§
ᑖḄ©ª
Ḅᐵ{pÑÒ$⚪Ḅᐵ&#ᳮ$⚪?ᮣÔÕᵨᡠÖÑÒ$×Ø⚪.e18⚓ᐳ18⚓