湖北省阳新县2022-2023学年数学八年级上册期末经典试题含解析

《湖北省阳新县2022-2023学年数学八年级上册期末经典试题含解析》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。

2022-2023
ᦪᔁ⚗1.⚪ὃᐜḄஹὃṹ"ᑏ$%ᩩ'ṹ()*ᙠᩩ'ṹ,-ᑁ஺2.⚪01ᢥ⌕4ᵨ6஺3.1ᢥ᯿⚪89ᙠ⚪ᓱᔜ⚪<Ḅ⚪,-ᑁ=>?⚪,-@ᑏḄᫀBᦔ;ᙠ₝FGஹᔁ⚪Bᦔ஺4.=JKᐜLᵨM6N?(OPQRᵨS⁐UVḄWU6XS஺5.Yᢝᓱ☢$\]⌕ᢚ_ஹ]⌕`ẚஹ`b]LᵨcᦋeஹfghஹiGᑐ஺kஹ⌱m⚪no⚪4ᑖᐳ48ᑖr1.᝞JᡠuvwxḄyw⚔{|ᙠyxḄk}Zl=30°,Z2=50°,ᑣN3nr30°C.40°D.50°2.᝞JAABCgAADE,AB=AD,AC=AE,ZB=28°,ZE=95°,NEAB=20°,ᑣNBADnA.77°B.57°C.55°D.75°3.Ḅy0.00000770.0000077ᵨᦪ⊤u
A.7.7x10-6B.7.7x10-5C.0.77x106D.0.77x1054.3-1ஹk'g(Ḅ
V1-4A—1B.yj],—aC.—y/1—ciD—y/a—\5.ᑡᩩḄ]ywvw'Ḅn
A.v}12GB.v}1C.vᑁw123vᑁw345

16.᝞Pm+3,2m+4
ᙠy{PḄᙶ᪗n
A.(-2,0)B.O-2
c.(i,o)D.(0,1)x-myB.yfc.y1=yD.]·(O229.¢|3x-2y-l|+Jx+y_2=0,ᑣ{x,y
ᙠ¸n
¹▲.A.»B.vC.~D.—10.ᙠJᡠuḄ¼½J'¾¿J'À¾¿ᨬÂḄJ'Ḅnra83b0஺+஺,11.᝞J-ABCNC=90஺4DÃᑖNBAC,Ä{஺=E,DC=4,ᑣOE=rJBDCA.3B.5C.4D.612.25ḄÃÅ᪷
A.±5B.5C.-5D.V?Çஹ"È⚪no⚪4ᑖᐳ24ᑖr13.᝞JÉNM8NᑁÊkO{PDA.BN,É஺=3,BD=1.Ä{PḄy²Ó8/Ë3NᑖÌÍÎ{EË{RA}Ïk{,Ä{A=ACLBN{C,ᨵAQ=3,ᑣ-3EF☢ÑḄᨬµ¬_____.BC

2MB14.᝞JᙠÔABCZACB=90°,CDÕNA=30஺,¢AB=20,ᑣBDḄÖ.15.᝞JᵬஹØÙÚÛÜÝᕒḄ10ßàáᡂãnᓫårḄᢚ²æçJèéJ'ᑏ?ᵬஹØê10ßÚÛᡂãëḄᜧµᐵ¶ìSn"“>"ᡈ16.᝞JÖÅ'ABCDAD=8,AB=4,BQ=5,{PᙠAD}ÜÝ
YBPQῪvw'0APḄÖ.17.᝞JÕÈòᓟḄuJµôõö÷åø{AᜐúḼ{OüÄᨬý{B,ᨬþ₩ᑮᨬCᜐ,NAOC=90஺ABḄAD=1BD=4ᑣCBḄCE.18.᝞ᙠA3C஺ZABC+ZDCB=90°,3c=2A஺ᑖ

3DC,BC,48ᔣ᜜#$%&'Ḅ☢)ᑖSiஹSzஹSi.$2=64,Si=9,ᑣSḄ+,ஹ-.⚪(ᐳ78ᑖ)19.(8ᑖ)᝞1,ᙠ
A5CZACB=90°,஺3cḄ2BE//AC.(1)345
45C6
OE5(1)78AOஹAE.CE,᝞1.জ345CE:NAC8Ḅ;ᑖ<=ঝ?ᑨA
A5E:BCᱯEFḄ,;GHIᳮᵫ.20.(8ᑖ)“MᐰᦟPQ”:SᦟPTU%VTWXTYZMᐰ[\]^ஹ_`Mᐰa⏨Ḅcdeᵨgh.i᪥kk-lWXTYZ“■nᦟP”Ḅopᙠq᪥TYrstuvᑖTY#wxyᦈ{Ḅᦪ}ᑖ~4o5A.TYZ=B.lWXTYcZ=C.lWZ=D.lWXTYZ.ᔜ:;<ᩩᓡ?@ᵨᔜ:;<ᡡCD@E(1)ᙠt᪵wxᐳwxkTY;

42
⊡ᐰᩩGᙠᡧCᡠeᡧḄᙊ;Ḅᦪ=3
᪷}t᪵wx8᪥2000TY“lWXTYZ”Ḅᦪ.21.8ᑖ:ᡃS¡¢ᨬ£⌕ḄᦪT℉#¦cᙠ“§¨”©ªkc⍝“ᢚ®ᙢ”°⚪:“²ᨵc´µᢚ®ᙢ¶q,·°ᢚὅ¹º»”¼½ᡂᦪT°⚪::᝞ᡠ¿ᙠAABC1NACB=90஺,AC+=10,3C=3,3ACḄW.22.(10ᑖ)ᓄÁ..(.1x2+2x+l(1)1-----------------IX+1)X11]9c3X-3x+32x'23.10ᑖ᝞AABC:Â,;D:BCÃc^E,FᑖᙠAB,ACÃ7_AD,DE,DF,NADE=NADF=60°.ÄIÅÆÇÈஹÉÊaËÌÍ5ᙠDÎ^ḄÆÏÐÑᨵAE=AF,ÄIyÒÌÍÓT'ÔÕÖ×ÅÆØÙᡂk4IÌÍḄ¹dÍÚ5ÍÚ1ᑭᵨAD:NEDFḄ;ᑖ<᪀⌼AADFḄᐰÂ,;ᯠßÅÆÂῪ,;Ḅáᐵ[\ã4.ÍÚ2ᑭᵨAD:NEDFḄ;ᑖ<᪀⌼;ᑖ<ḄឋåæᳮḄçqᯠßÅÆᐰÂ,;Ḅáᐵ[\ã4.ÍÚ3è4ACDéAêë┐íîï-ABG,ðñACXAB£ᔠᯠßÅÆᐰÂ,;Ḅáᐵ[\ã4.?óZὃÃ☢ḄÍÚõöÄI4IAE=AF.÷cd%Úᓽù24.10ᑖÄIX᱆᱆ᕜµᑮüᙢýþÔÕÿ

ᒴᐳᓫᑮᐭ
ᯠᒴᑮ
ᑮḄ᱆᱆"ᓽ$ᐳᓫ

5ᢥ᯿ᩭ)*+,-
ᙠᐭᜐᦋ1
2ᢥᩭ)*+-,ᑮ⌹ᶇ610ᑖ89-
᱆᱆ᙠ:;<=>ᙢḄ+<@ḄAḄBᦪᐵE᝞G.(1)G=m=,n=I(KLᑏNO)(2)Q⌕ᙠ᱆᱆ᑮ9STU
V-)WXYZX[kmo\1020W~^]^25.(12ᑖ)_☢ᑁḄᩩKcᨵefg_hijᐵE(1)᝞Ga,QAB஻CD,kPᙠABஹCD᜜n
ᑣᨵNB=/BOD,$pNBODY
PODḄ᜜q
ᦑNBOD=NBPD+ND,sNBPD=NB-ND.tkPuᑮABஹCDᑁn
᝞Gb,vUNwYᔲᡂ"[Qᡂ"
zᳮᵫIQ}ᡂ"
ᑣNBPDஹNBஹND9Aᨵ~ᦪᐵE[ḄNwI(2)ᙠGb=
tKcABkB⌮┐ᔣq)fKcCDkQ,᝞Gc,IJNBPDஹNBஹNDஹNBQD9Aᨵ~ᦪᐵE[(}◤)(3)᪷(2)ḄNwGd=NA+NB+NC+ND+NE+NFḄ)ᦪ.26.ᓄ[(a+2b)(a-2b)-(a+4b)2]-r(4b).ὃᫀஹ⌱⚪(⚪4ᑖ
ᐳ48ᑖ)

61ஹAூᑖ᪆௃ᐜ᪷_cḄឋ¡sᑮN4=N2,ᯠ᪷¢q£᜜qḄឋ¡ᨵN4=N1+N3,ᨬᑭᵨN3=N4—N1ᓽ§¨.ூ©¨௃᝞GvZ4=Zl+Z3,Zl=30°,AZ3=Z4-Z1=50°-30°=20°.ᦑ⌱A.ூkª௃«⚪¬⌕ὃ_cḄឋ¡®¢q£᜜qḄឋ¡
¯°_cḄឋ¡®¢q£᜜qḄឋ¡Y¨⚪Ḅᐵ±.2ஹAூ¨᪆௃²⚪ᑖ᪆•.,-ABCgZkADE,NB=ND=28°,XVZD+ZE+ZDAE=180°,ZE=95°,:.ZDAE=180°-28°-95°=57°,VNEAB=20஺
´ZBAD=ZDAE+ZEAB=77°.ᦑ⌱A.ὃkᐰ¶¢q£Ḅឋ¡3ஹAூᑖ᪆௃·¸¹1Ḅºᦪ»§vᑭᵨ¼½¾ᦪ¿⊤Á
£Ã1axlOZ@ÄᜧᦪḄ¼½¾ᦪ¿}ḄYᐸᡠÈᵨḄYÉᢣᦪË
ᢣᦪᵫ*ᦪÌÍÎÏÐ}1ÑḄᦪÒS☢Ḅ0ḄÐᦪᡠÓ.ூ©¨௃¨0.0000077=7.7x101.ᦑ⌱A.ூkª௃

7K⚪ὃNᵨOPQᦪS⊤UVWḄᦪYZ[\]axio,ᐸ`lw|a|V10,n]ᵫdᦪefghYij]kḄᦪlm☢Ḅ0Ḅiᦪᡠpq.4ஹCூt᪆௃ᐜ᪷yz{᪷\ᨵ}~ᨵᩩl-a>0,ᵫᑭᵨz{᪷\Ḅឋᓄᫀ.ூt௃•'z1ᨵ}~,V-a1-a>0,<7—1<0,ᦑ⌱C.ூ௃ὃNz{᪷\Ḅឋᓄᓄz{᪷\t⚪ᐵ.5,Dூt᪆௃᪷y[ᑁqᳮ¡qᳮḄ⌮qᳮᑨqᔲ]¥[.ூt௃tA,12+(V3)2=22,¦ᔠ¡qᳮḄ⌮qᳮᡠ¨¥[©B.12+(72)2=(^)2,f¦ᔠ¡qᳮḄ⌮qᳮᡠ¨¥[©Cஹ᪷y[ᑁqᳮ«hi]90°,ᡠ¨[¥[©Dஹ᪷y[ᑁqᳮ«ᔜᑖ]45°,60°,75°,ᡠ¨[j¥[©ᦑ⌱D.ூ௃K⚪ὃN¡qᳮḄ⌮qᳮ᝞¯[Ḅf°a,b,c±²a2+b2=c2,³´µi[¶¥[.·ὃN[ᑁqᳮ.6ஹBூᑖ᪆௃᪷yᙠy¹º»¼PḄ½ᙶ᪗]1,ᓽ»mḄÁqPḄᙶ᪗ᓽ».ூt௃t•••P(m+3,2m+4)ᙠy¹ºm+3=0tm=-3,

82m+4=2x(-3)+4=-2...PḄᙶ᪗(b-2).ᦑ⌱B.ூ௃tpK⚪ḄᐵQÂy¹ºḄᱯ½ᙶ᪗]1.7ஹDூᑖ᪆௃✌ᐜqjÅ\ÆḄtÇᐜᑭᵨÈÉḄ\Ê⊤U᪷y᦮ᦪtḄiᦪ¶»¨qᨵÌÍ᦮ᦪt᪷ytḄ;<»¨ᑮᐵÏ”ḄjÅ\ÑÒ«”ḄÔ.ூt௃tÕ.zஹᵫ(1)xè2ᦑ⌱A.ூ௃⚪ὃNY{éᦪḄäæឋêQéᦪḄឋqᳮᓽ»t⚪.9ஹDூᑖ᪆௃ᑭᵨëìᦪḄឋᑡíîÆ«íîÆḄtᑮxyḄÁᓽ»q

9ᡠᙠḄï▲.ூt௃t'\3x-2y-]\+ylx+y-2=0,.j3x-2y-l=0*[x+y-2=09x=1t\,[y=iᑣ(i,i)ᙠhYï▲ᦑ⌱D.ூ௃K⚪ὃNtzᐗY{íîƨâëìᦪḄឋḄᙶ᪗êö÷øíîÆḄtSt⚪Ḅᐵ.10ஹAூt᪆௃᪷y¹ùúû[Ḅq~ᙠü☢ᑁýYᩩ¥þᢚ
ḄᑖᐰᔠḄ
ᩩ
⌲ᑨᓽ.ூ!"௃A⌱⚗
&
ᨵ4ᩩ(B⌱⚗
&
ᨵ2ᩩ(C⌱⚗
)&(D⌱⚗
&
ᨵ3ᩩ(ᦑ⌱+A.ூ,-௃.⚪0⌕ὃ345Ḅᳮ"
789:
ᓽ"⚪.11ஹCூᑖ᪆௃᪷?@AᑖBḄ,ᑮ@ḄDḄEFGH"Iᓽ.ூ!"௃TADAᑖNBAC,DEJLAB,ZC=90°,CD=4,.,.DE=CD=4,ᦑ⌱+C.ூ,-௃.⚪ὃ3@AᑖḄឋK
9:@ḄAᑖBḄ,ᑮ@ḄDḄEFGH&"⚪ḄᐵM.12ஹAூᑖ᪆௃᝞PQᦪxḄASHTa,UVx&a&AS᪷
᪷?.Wᓽ"⚪.ூ!"௃V(±1)2=21

10.21ḄAS᪷±1.ᦑ⌱+A.ூ,-௃Y⚪0⌕ὃ3ZAS᪷W
ᐵM&[\Q]ᦪᨵQAS᪷.^ஹ_`⚪(b⚪4ᑖ
ᐳ24ᑖ)13>24ூᑖ᪆௃᝞
eEH_LBNfBNT,H,ᐜhijBHE~z!\BCA,ᯠlmBH=t,noiᑮEH=3t,HD=1-t,pᳮiaEPDqjFEH,ris=u=!,noriHFEHtBF=BH+HF=gᨬl᪷?£"=*
|f—l=x
iᑮS…`B1=/424224.XXூ!"௃"+᝞
eEHLBNfBNT,H,■:AC1BN,AEH//AC,AABHE-ABCA,.AC_EH஺BCBHmBH=t,ᑣEH=3t,HD3D-BH=l-t,PDBN,.,.EH//PD,.••jFPD-AFEH,.DFPD3I,,7HF=DF+DH=DF+(5-t)DF1•_______________———■"DF+(5-t)~tt.DF=DF+(5—t)5-f"i+DF=-.HF=^+(5-t)=»(5-t),t5—t4f:.BF=BH+HF=t+——(5-0=r(l+——)=——,t-\t-\t-\

1114rC6r=-BF»EH-----------3/22t-1|l=x,ᑣ%=2"Xo(+1)2=(1)2+4X,ÔÕ—+24*xx.ABEF☢Ḅᨬ&24,ᦑIᫀ+24.ூ,-௃Y⚪ὃ3G@ḄឋKᑨᔠ⚪,"⚪ḄᐵM&᪷?G@ḄឋK᪀ᔜDḄᐵ
45ᵨᣚᐗrᦪḄᨬ.14ஹ1ூ!"௃⚪ᑖ᪆+᪷?p@Ḅ@GH¡
ZBCD=ZA=30°,ᡠ4ᑖ£ᙠjABC¥
BDC¦ᑭᵨ30஺┦@ᡠḄ@DHTªDḄ«ᓽr¬BD.":,ᙠ@AABC¦
ZACB=90°,ZA=30°,®CD_LAB.•.ZBCD=ZA=30°,VAB=20,11.,.BC=-AB=20x-=10,2211/.BD=-BC=10x-=l.22ᦑIᫀ1.ὃ,+¯30°@Ḅ@@.15ஹ±ூᑖ᪆௃S²³ᜧ
ᑣAᙳḄFᦣ·°³ᜧ
¸ឋ¹³(º»
ᑣ¼ᐸAᙳḄFᦣ·°³
¸ឋ³¾
ᑨ¿ᓽ.ூ!"௃"+ᵫi
ᵬ10ÂÃÄᡂÆFᦣ·°
oÇ10ÂÃÄᡂÆFᦣ·°ᜧ,

12:.⏑

13VCQ=3,CD=4,.•.᪷?ØÙᳮ
PQ=5=BQ,.ßAP=AD=1,Bᡠå
áVBPQHῪ@ß
APḄæ3ᡈ3ᡈ2ᡈ1(2ᦑIᫀ+3ᡈ&ᡈ2ᡈ1.2ூ,-௃.⚪ὃ3Ḅ&ÑḄឋKஹHῪ@ḄឋK¥ØÙᳮ
9:ÑḄឋKஹHῪ@ḄឋKஹᑖÕÖ×Ḅᦪè¥ØÙᳮ&"⚪ᐵM.17ஹ4.1ூᑖ᪆௃᝞(é"᪆)
ê,Aeê,Ce஺G_LQ8,ᐜᑭᵨØÙᳮr¬OAḄæ
ë᪷?@ᐰHḄᑨᳮឋKr¬OGḄæ
ᨬl᪷?ìḄ¥²ᓽi.ூ!"௃᝞
ê,AeAH_LQB,ê,CeCG_LQ3,ᑣÝDADBH¥ÝDCEBGí&Ñᵫ⚪\i
OA=OB=OCᵫÑḄឋKi
AH=BD=4,BH=AD=1,CE=BGᙠmAAHO¦
+gp(OB-BH)2+AH2=OA217î!](QA—1)2+42=஺42,"i04=3=8.5vZ2+Z3=Zl+Z3=90°.•.N2=N1•ð4OGC=ZAHO=90°,OC=OA\OGC=^AHO(AAS)OG—AH—4:.BG-OB-OG=OA-OG=8.5-4^4.5ᑣCE=3G=4.5ñòóᦑIᫀ+4.1.

14ூ,-௃Y⚪ὃ3ZØÙᳮஹ@ᐰHḄᑨᳮឋKஹÑḄᑨឋKH¡Û,
ôêeõö
᪀⌼QᐰHḄ@&"⚪ᐵM.18ஹ2ூᑖ᪆௃ᵫø¡4iᑮ+S3+\=S2,ᐭᔜúûüý4iᑮ"I.ூ!"௃"+᝞
êAeAE஻DCfBCTE,
îþ⚪\¡/ABC+NAEB=90஺
BE=AD=-BC,AE=DC,2^@ABE&@@
.•./ÿ2+2=3£2,ᓽAB2+DC2=-BC2,4S3+S]=%S,,S3——S-,—Sj=—x64-9=7,ᦑᫀ2.ூ௃⚪ὃஹ☢ᳮḄᔠᵨ"ᵫ$%&ᑮ()☢Ḅᐵ+,-.⚪ᐵ/.(ஹ.⚪1ᐳ78ᑖ419ஹ1
56.᪆81
জ56.᪆8ঝaABE-:Ὺ(<"ᳮᵫ56.᪆.ூ.᪆௃1ᵫAC//BE,NACB=90஺>&NDBE=90஺"ᵫAC=?BC,D-BC@2>&AC=BD,ᑭᵨHLᓽ>BCAABCg/SDEB1
জᵫ1
&BE=BC,ᵫ:ῪD<(<ḄឋF>&NBCE=45஺"GH>&NACE=45஺"ᓽ>&ᫀ8ঝ᪷KSAS

15§AACEØZkDCE,§sAE=DE,ᵫAB=DE§sAE=ABᓽ§AABEY¶Ὺ¢q£.ூ©¨௃(1)VZACB=90°,BE/7AC:.ZCBE=90°´AABCgADEBÚYKq¢q£VAC=-BC,kD1BCḄ=k2/.AC=BD$TABuDE.'.
ABC^ADEB(H.L.)(1)জᵫ(1)sAABC^ADEB/.BC=EB$NCBE=90஺ZBCE=45°:.ZACE=90°-45°=45°:.NBCE=NACE...CEYNACBḄq_ᑖcঝAABEY¶Ὺ¢q£
ᳮᵫ᝞ÜAC=DCᙠAACEgADCE=

16ூ௃⚪ὃᐰ:(<ḄᑨឋFO:Ὺ(<ḄᑨPឋF"QRSTᑨᳮ-.⚪ᐵ/.20.(1)400(2)⊡ᐰᩩW6.᪆8CXᡠZᡧḄᙊ]<Ḅ^ᦪ54஺8(3)`᪥2000bcd@“fghcdijk”ᨵ100n.ூ.᪆௃ᑖ᪆o(1)᪷KAXpnᦪOᐸᡠᓰsᑖt>&unᦪ8(2)unᦪvwAஹCஹD()Xpnᦪx&BḄnᦪᓽ>⊡ᐰᩩW"yᵨ360஺z{CXpnᦪᓰ|}nᦪḄt~>&8(3)ᵨunᦪz{᪵@DXpnᦪᡠᓰt~>&.5.o(1)}Ḅunᦪ80+20%=400n8(3)`᪥2000bcd@“fghcdijk”Ḅnᦪ2000xF=ON=100n.No⚪ὃᩩWஹᡧWOᵨ᪵uḄ%".⚪Ḅᐵ/-W@᦮ᳮG.⚪Ḅ.21ஹAC=4.55ூᑖ᪆௃ᙠRtAABC@ᑭᵨᳮᓽ>xAC.ூ5.௃VAC+AB=10

17.*.AB=10-ACᙠRtaABC@"AC2+BC2=AB2ᓽAC2+32=(10-AC)?.&AC=4.55ூ௃⚪ὃᳮḄᵨ"ᑭᵨᳮ-.⚪Ḅᐵ/.322ஹ(1)x+1(2)--------,x+3ூᑖ᪆௃(1)ᐜᑁḄᑖ,Ḅv"yz",ᑖ.ᑖ>{.⚪;(2)ᐜᑁḄᑖ,Ḅ"yz",ᑖ.ᑖ>{.⚪.22x+1ூ5.௃.o(1)LV+Ix+1)x_X+l-1(x+l)2x+1X_xx+11X=x+lফf1I19-3X(x-3x+3)2xx+3+x—33(3—x)(x+3)(x-3)2x2x3x+32x3x+3ூ௃⚪ὃᑖ,Ḅᑣᔠ,STᑣh¡¢-ᐵ/.23ஹ6.᪆ூ.᪆௃£1ᙠDE¤¥¦DG=DF,§¨AG,ᐜᑨ
ADG^^ADF,&ᑮAG=AF,y᪷KNAEG=NAGE,&AE=AG,GH&©ªJAE=AF£2«A¬AGLDEG,AH_LDFH,®K<ᑖ¯ḄឋF&ᑮAG=AH,GHᑨ
AEGg^AFH,ᓽ>&ᑮAE=AF£3°4ACD±ḼA¡³┐µ¶©
ABG,·&ACAB¸ᔠ"§¨DG,ᑨ4AGD-:(<"GH&
AGE^^ADF,ᓽ>&ᑮAE=AF.

18ூ5.௃BCo£1:᝞W"ᙠDE¤¥¦DG=DF,§¨AG,VAABC-:(<"/.ZB=ZC=60°,VZADE=ZADF=60°,AD=AD,.•.AADG^AADF,.•.AG=AF,Z1=Z2,VZADB=60°+Z3=60°+Z2,N3=N2,.•.Z3=Z1,,.,ZAEG=60°+Z3,ZAGE=6O°+Z1,:.ZAEG=ZAGE,.*.AE=AG,.*.AE=AF£2᝞W"«A¬AG_LDEG,AHJ_DFH,.*.AG=AH,VZFDC=60°-Zl,:.ZAFH=ZDFC=6O°+Z1,VZAED=6O°+Z1,/.ZAEG=ZAFH,

19/.ºAEG^AAFH,/.AE=AFâ¿3᝞G
taACDḼkAä┐W^ARG,ÈsAC@ABåᔠ
çLDG,.AG=AD,ZGAB=ZDAC,VAABCY¶Í¢q£
:.ZBAC=ZABC=ZC=60°,:.ZGAD=60°,...
AGDY¶Í¢q£
.e.ZADG=ZAGD=60°,VZADE=60",AG,E,D¢kᐳc
.•.AAGE^AADF,AE=AF.ூkª௃«⚪ὃ6ᐰ¶¢q£Ḅᑨ@ឋ¡v®¶Í¢q£Ḅឋ¡
¨⚪Ḅᐵ±YéêḄ¯°ᐰ¶¢q£Ḅᑨ@ឋ¡v®¶Í¢q£Ḅឋ¡.24ஹ125,12-)WXY0.2ᓟì/ᑖ.ூ¨᪆௃1᪷BᦪGî
ᐜ᱆᱆ᐳᓫḄ)v®ᒴḄ)
ï,-⌶=᱆᱆ᑮᐭḄA
sᑮmḄ¹Iᯠ᱆᱆ᐭᑮḄA
ñòsᑮnḄ¹I2᪷⌕ᙠ᱆᱆ᑮ9STUsᑮ}¶ᐵEn-᱆᱆ᑮḄA-ᑮ⌹ᶇḄ10ᑖ8ôx-Ḅ)9@Ḅõ>
ö÷ᑡ}¶Ã
¨ᓽ§.2ூ©¨௃1ᵫ⚪ù
§s᱆᱆ᐳᓫḄ)1-=0.2ᓟì/ᑖô

20᱆᱆ᒴḄ)1—~-=0.1ᓟì/ᑖô
20-103-2,-⌶=᱆᱆ᑮᐭḄA1——=5ᑖ8ô
0.2ᡠvm=20+5=252᱆᱆ᐭᑮḄA161=20ᑖ8ô
ᡠvn=25+20=l.ᦑᫀ125,12
ú-)Yxᓟì/ᑖ
᪷⚪ù
s1-25-10
x22,¨sx>0.2.-)WXY0.2ᓟì/ᑖ.ூkª௃«⚪ὃ6ûBᦪḄüᵨ
ᐗû}¶ÃḄüᵨ
+<ஹ)@AᐵEḄüᵨ,ᳮ¨⚪ù
Gî=þÿᨵᵨ⚪Ḅᐵ.25ஹ1
ᡂ.NBPD=NB+ND,᪆2
ZBPD=ZBQD+ZB+ZZ3
360°.ூᑖ᪆௃1
BPCDE,᪷!"#$ᑁ┯'()$*+NPED=NB,,ᑭᵨ.'/Ḅ01᜜')34(5Ḅ1ᑁ'Ḅ3ᓽ78ᡂ$9:ZBPD=ZB+ZD2
;7?3
᪷@A/Ḅᑁ'3BC2
Ḅ*ᓽ7.ூD௃E1
ᡂ.NBPD=NB+NDBPCDFE,VAB/7CD.\ZB=ZBEDGINBPD=NBED+ND,.*.ZBPD=ZB+ZD.2
EZBPD=ZBQD+ZB+ZD.;

21(3)ᙠ@A/CDFGM$ZCGF+ZC+ZD+ZF=360°,GNAGB=NCGF,,ZAGB+NC+ND+NF=360°,ᵫ(2)O$NAGB=NB+NA+NE,ZA+ZB+ZC+ZD+ZE+ZF=360°.ூFP௃Q⚪ὃSḄ"#!Ḅឋ>$.'/Ḅᑁ'$.'/᜜'Ḅឋ>$BCTA/Ḅᑁ'3,᪷⚪V;+WX!$᪀⌼+.'/$ᑭᵨ.'/᜜'Ḅឋ>*[\⚪Ḅᐵ.26ஹ-5)-2a.ூᑖ᪆௃᪷⚪Vᐜ^_`aᑁḄ$,^_◀cᓽ7?+[ᫀ.ூD௃E[(a+2b)(a-2b)-(a+4b)2]v(4b)=(a2-4b2-a2-8ab-16b2)-r(4b)=(-20b2-8ab)v(4b)="5b-2a.ூFP௃Q⚪e⌕ὃS᦮hḄiᔠk_,⚪Ḅᐵlmnᐰ"pqh3"prqhCᔠstu⚗cᑣ.