=;$;px :8x =p :6 m =+ =p_ +p =44p+56p=00p cm + ={;$;p_5 }_;!;+(p_5 _)_;!; 50p 00p ={ + } =: ;%;º:p cm 5cm 4 OO O OO O =60 AOF =60-90 -90-60 =0 BO C= DO E=0 μaf+μbc+μde+ab +CD +EF = +OO +O ÚO +O ÚO =8p+8_=8p+4 cm 5 _;8&;+ _ =(4p_4 )_;8&;+{;4!;_p_4 }_ =56p+p=68p cm 6 - ={;$;p_8 }_;!;-{;$;p_4 }_;!; 04 8 896 = p- p= p cm m cm cm B A C O F O O D E - A - B= C A+ B+ C=80 A+70 +70 =80 A=40 - A=x ACB=x 40 CBD ABC CBD=x BCD ADC=x DCF= A+ ADC, 0 =x+x x=0 x=40 A=40 40 - BAD ACE(RHA ) DA =CE = cm AE =BD =4 cm BCED E D =D A +A E =7(cm) (+4)_7 BCED= 555555555555 =: ª:(cm ) -4 BC =AC =8 cm, BE =6 cm EC =BC -BE =(cm) ACE ADE(RHS ) DE =EC =(cm) : ª:cm cm -5 ABC M A M =B M =C M ABM BAM= B=0 AMC= B+ BAM=0 +0 =60-6 O BAO+ CAO+ BCO=90 BCO=90-40 -0 =0 BOC=80 - BCO- CBO =80-0 -0 =40 60 40 8 _
-7 ABC= ABI+ BCI+ ACI ABC=AB ;!;+BC ;!;+AC ;!; ABC=AB +BC +AC =0(cm ) 0 BM =CM yy AM BC yy OBM OCM SAS yy BM =CM OMB= OMC=90 OM OBM= OCM ABM= ACM yy 0 BCE BDE C= D=90 C E =D E B E BCE BDE(RHS ) B=0 CBE= DBE CBE=5 BEC=80 - CBE- C BEC=80-5 -90 =75 0 DEF= GEF AD BC DEF= GFE( ) EGF EG =GF 0 cm -8 I MBI= CBI, NCI= BCI MÚN BC MIB= CBI, NIC= BCI MBI, NCI AB =AM +B M =AM +MI AC =AN +CN =AN +NÚI AMN A MÚ+MÚNÚ+A NÚ=A MÚ+MÚI +IN +A NÚ =AB +AC =4+6=0(cm) 0 cm EGF=( )_( )_;!; EGF=4_0_;!; EGF=70(cm ) 04 BEF BCF E= C=90 FBE= FBC B F BEF BCF(RHA ) EF =CF DEF DEF=90, EDF=45 DEF DE =EF DE +DF =EF +DF =CF +DF =6(cm) 05 I AFI AEI BFI BDI CDI CEI AF =AE, BF =BD, CD =CE AB =AF +BF =AE +BF 5=+BF BF =(cm) EC = cm BC =BD +CD =BF +CD BC =BF +EC =+=4(cm) 06 AO =BO =CO AO =x BOC BC +BO +CO =5+x+x= x=8, x=4(cm) AO =4 cm 70 cm 6cm 4cm 4cm 07 A B _;!;=0_;!;=5(cm) 08 ABC= ABI+ BIC+ AIC ABC=6 ;!;+8 ;!;+4 ;!; ABC=+4+=9(cm ) 5cm 9cm _ 9
- - BD B ABD= CBD AD BC ADB= CBD ABD AB =AD ABCD ABCD - AP BC CBP= APB) ABP AB =AP PD =AD -AP =BC -AB =8-6=(cm)) -4 B= DD+ C=80 60 + C=80 C=0 DCE=60 D=60 E=60 EDF=80 -( DEF+ DFE) =80 -(90 +60 )=0 cm - BO =DO, BO =BE =E OÚ BD =4E OÚ=4_5=0(cm) 0-5 AD AE BEA= EAD=90 AED AED= ADE=45 A DÚ=A E (4+0)_4 ABCD= 5555555555555555=8(cm ) -6 AB CD ACQ= BCQ AC PQ AQC= APC AD BC APC= ABP AQC= BCQ= APC= ABP 0 cm 0 90 90 0, 0 ABCD=6_ ABE ABE= ABCD_;6!; ABE=4_;6!;=7(cm ) 04 A B C DÚ BAC= ACD ( ) A C =A DÚ ACD= ADC=5 CAD=80 - ACD- ADC CAD=80-5 -5 =0 7cm 0 05 06 ABF CBF A B =B C, ABF= FBC=45, B F ABF CBF(SAS ) AFB= CFB AFC=80 - CFE=80-40 =40 AFB=40 _;!;=70 AFB= DAF+ ADF 70 = DAF+45 DAF=70-45 =5 07 B= D D=60 AB =CD ED =CD E= C CDE CE =5 cm 5 5cm 08 AE CD AED= AEC ABED= ABE+ AED 0 _
= ABE+ AEC = ABC=0 cm O ABC OA =OB =OC OCAOBA 5 + OBC+7 =90 OBC=8 I ABC IAB= IAC=40, IBC= IBA= A+ B+ C=80 80 +46 + C=80 C=54 x=54 A+ B+ C = x+ y+ z A= x+ y=80 80 =( x+ y)+ z =60 + z z=0 z=0 OBC=0 4 0 cm BCI=BC _( )_;!;=4 ( )=6(cm) 8 54 0 ABC A I ABC= ABI+ AIC+ BCI ABC=5_6_;!;+6_6_;!;+4=57(cm ) 8 : 4=9 : x x=57(cm ) 57 cm 6 7 8 9 AB =0(cm) 0 cm AC r r=ac _;!;=5(cm) pr =p_5 =5p(cm ) 5p cm A DÚ B C DAE= AEB ( ) ADF= DFC ( ) ABE, DFC AB =B EÚ=8(cm), CD =C F =8(cm) E F =B C -B F -C E =0--=6(cm) 6 cm ABCD A= C B= D A B A D B C A+ B=80 A: B= : 5 A= 55_80 =0 +5 B=80-0 =50 C=0, D=50 C=0, D=50 ABD CBD A B =B C A DÚ=DC A= C( ) ABD CBD(SAS ) DBC= DBA=0 CBD BDC= DBC=0 C=80 - BDC- DBC =80-0 -0 =0 0 5 AO =CO ACO= OAC=60 AOC 0 D A B B C M CDM C M =5(cm) ABMD _
B M =5(cm) B C =B M +C M =0(cm) 0 cm -4 ABC ADE A ABC= ADE( ) ABCª ADE(AA ) - - ABCª DEF B= E=40 DEF D+ E+ F=80 D+ F=80-40 =40 A C : DF = : A C : 5= :, A C =0 A C =0(cm) A D+ F=40, AC =0 cm B EÚ=x AB :AD =AC : AE (6+x) : 4= : 6 6(6+x)=4_ x=(cm) -5 B H =x A B =B HÚ_B C 8 =x_0 x=6.4(cm) B H =x A C =C HÚ_C B 5 =_(+x) x=: :(cm) 6.4 cm : : cm - ADE ABC AD : AE =5 : 4 AB : AC =0 : 8=5 : 4 A ADE ª ABC(SAS ) - ABC DAC B= DAC, ACB= ACD ABCª DAC(AA ) ADE ª ABC SAS 0 ABC DBE C= BED, B ABC DBE A B : B C =D B : B E 6:BC =:4 BC =4, BC =8(cm) C DÚ=B C -B DÚ=8-=5(cm) 5cm 0 ADCª BDH A DÚ : B DÚ=D C : D HÚ A D : 6=6 : ABCª DAC A C : D C =B C : A C 6:4=x: 6 x=9(cm) B DÚ=B C -C DÚ=9-4=5(cm) ABD=B DÚ_A HÚ_;!; 0=5_A HÚ_;!; A HÚ=4(cm) A D =6, A D =(cm) A HÚ =A DÚ-D HÚ=-=9(cm) 0 BAH ACH H ABH= CAH BAH ª ACH(AA ) B AÚ : A C =A HÚ : C HÚ AC _AH 5_ C HÚ = 54444444= 544=9(cm) BA 0 9cm 9cm _
04 : A DÚ : B DÚ = :, A DÚ : 4= : A DÚ=(cm) B D =A DÚ_C DÚ 4 =_C DÚ C DÚ =8(cm) 05 ABC ACD A ABC= ACD ABCª ACD(AA ) AC : AD =BC : CD 6:4=BC :8 BC =(cm) AB : AC =AC : AD AB : 6=6 : 4 AB =9(cm) ABC AB +BC +AC =9++6=7(cm) 06 ABC DBA A B : D B =6 : 4= : B CÚ : B AÚ=9 : 6= : B ABC ª DBA AB : DÚBÚ=AC : DÚAÚ 6:4=5:DÚAÚ DÚAÚ=0 D AÚ=: º:(cm) 07 ACB ABD A ABD= BCD ACBª ABD(AA ) AB : AD =AC : AB : 8=(8+x) : 8(8+x)=44 x=0(cm) 8cm 7 cm : º: cm 0 cm B AÚ : B E =B D : B C, 9 :(9+x)=6:0 54+6x=90, 6x=6 x=6(cm) - - B C D E 6 : (6+x)=0 : 5 60+0x=90, 0x=0 x=(cm) - B C D E A B : A DÚ=A CÚ : A EÚ 6 : 4=8 : x, 6x= x=: :(cm) - l m n A C : B D =C E : D F x:6=(x-4):4 x-4=4x 8x=4 x=(cm) C E =x-4=_-4=(cm) -5 G ABC A GÚ : G DÚ= : A GÚ =A DÚ_;@;=8_;@;=(cm) 6cm cm : : cm A C = cm, C E = cm -4 DEF D E +D F +E F =6(cm) B C =D F, A C =D E, A B =E F ABC A B +B C +A C =(E F +D F +D E )=(cm) ABC= ABG= AGC= BCG ABC=_ ABG=_4=7(cm ) cm AG = cm, ABC=7 cm 08 C A D BA E ABD EBC AD EC BAD= BEC() B ABDª EBC(AA ) ACE ACE= AEC AE =A C =x -6 AODª COB A DÚ : B C = : 5 AOD : COB= : 5 6: COB=9 : 5 9 COB=50 COB=: º:(cm ) : º: cm _
-7 : 6 cm, 8cm V V=pr h=p_6 _8=88p(cm ) p_ _4=6 p(cm ) : =6p`: V V= _6p=88p(cm ) 88p cm E F =: 8º: E F =: 4 :(cm) 0 l m n A C : B DÚ=C E : D F 4 : 6=0 : x, 4x=60 x=5(cm) : 4 : cm 5 cm -8 : 0000=5 : x x=50000(cm)=500(m)=0. 5(km) 0.5km 04 B GÚ : E GÚ= : DBG= DGE DBE= DGE -9 0 km=0000 m=000000 cm 000000 : x=50000 : 50000x=000000 5x=00 x=40(cm) 40 cm AD =DB ABE= DBE ABC= ABE=4 DBE= DGE ABC=_4=48(cm ) 05 48 cm D E =;!;A B E F =;!;B C 0 ABE CDE A B C D ABE= CDE( ) BAE= DCE( ) ABEª CDE(AA ) A E : C EÚ=B E : D E 6:x=4:6 x=9(cm) 0 EFG ECD F G CD EFG= ECD() EGF= EDC() EFGª ECD (AA ) F G : C DÚ=E G : E D =: F G =;!; C DÚ=;!;_0=5(cm) ABE GFE A B F GÚ ABE= GFE( ) A B F GÚ BAE= FGE( ) ABE GFE(AA ) A B : F GÚ=BE : EF 8:5=6:EF 8E F =0 9cm F DÚ=;!;A C D E +E F +F DÚ=;!;(A B +B C +A C ) D E +E F +F DÚ=;!;_6=8(cm) 06 G ABC ABC=6 GBD GBD=4 6=4(cm ) 8 cm 4cm 07 D B C AC M DFM EFC C F =MÚF =x A M =C M =x A F =x=(cm), C F =4(cm) x=4(cm) 08 ADE, AGF, ACB :: : : = : 4 : 9 ADE : DFGE : FBCG = : (4-) : (9-4)= : : 5 DFGE : FBCG= : 5 DFGE : 0= : 5, 5 DFGE=90 DFGE=8(cm ) 4cm 8 cm 4 _
AEFª CBF A E : B C =A F : C F A E :0=:5 A EÚ=6(cm) x=a DÚ -A E =0-6=4(cm) ABCª EDA A B : E DÚ=A C : A E 8:4=(5+x):5 x=5(cm) ABC A H =B HÚ_C HÚ=4_9=6(cm) A HÚ=6 cm ABC=B C _A HÚ_;!;=(4+9)_6_;!;=9(cm ) 4cm 5cm 9 cm 7 8 (P )=()_+() (P )=p_ _+p 5 (P )=8p(cm ) P Q : : =4 : 9 4 : 9=8p:(Q ) (Q )=6p(cm ) 6p`cm P;@; Q (P+Q) Q : : =7 : 8 P: Q =(7-8) : 8=9 : 8 P : 6=9 : 8 P=8(cm ) 8 cm 4 AC MÚN P MÚP =;!; B C =5(cm) 5 NÚP =;!; A DÚ=(cm) MÚNÚ=MÚP +NÚP =8(cm) A GÚ : G DÚ= : G DÚ =;!;A DÚ=;!;_8=6(cm) 8cm 0 0 0 04 0 05 06 6cm 07 08 09 0 4 5 6 7 60 cm 8 cm 9 ::0 : 9cm :5 000 4 ;6!; 0 G G' : G 'D = : G G' =;@;_G DÚ =;@;_6=4(cm) 0 4cm 6 AODª COB 6:9=: AOD : COB= : : COB=4 : 9 COB=7(cm ) AOD DOC : AOD : DOC= : : DOC= : DOC=8(cm ) BCD= COB+ DOC BCD=7+8=45(cm ) 5cm DCE DEC= DCE=70 CDE+70 +70 =80 CDE=40, ADE=0 DAE=x DAE 0 +x=80 x=5 0 O ABCOC OBC OCA _ 5
C= BCO+ OCA=0 +5 =55 0 ABE BCF BAG= CBF ABG+ BAG= ABG+ CBF =90 04 AB =AC ABC= ACB=;!;(80-40 )=70 ABD= CBD=5 ACB=70 ACE=0 ACD= DCE=55 DBC DBC+ x= DCE 5 + x=55 x=0 05 ABC A C =B C B=45 BDE BDE=90 BED=45 BDE B DÚ=D EÚ ADE ACE B DÚ=D EÚ=E C B=45 DAE= CAE AEC=90 -.5 =67.5 06 C A D B A E AEC= FAD ACE= CAD AEC A EÚ=A C EBCª ABD B EÚ : B C =A EÚ : C D, C DÚ=6(cm) 4 : 6=4 : C DÚ 07 ABE= ABC- EBC=90-60 =0 ABE BEA= BAE BEA+ ABE= BEA+0 =80 x+0 =80 x=75 BEA=75 08 ABD CAE B D Ú=A E, A DÚ=C E C E +B DÚ=D E, CE =4-8=6(cm) C E =6(cm) 09 O ACO= CAO BCO= CBO ABO= BAO ACO+ BCO+ ABO=90 ABO=90-0 -0 =40 x=80-40 _=00 0 AOB+ BOC+ COA=60 AOB : BOC : COA= : : 4 AOB=;9@;_60 =80 BAO= OBA x=(80-80 ) =50 I BAI= CAI ACI= BCI CBI= ABI BAI+ ACI+ CBI=90 BAI=90-40 -0 =0 I ID =IE =IF I ABC = ABI+ BCI+ ACI =(A B +B C +A C )_;!;_4 =(A B +B C +A C )_ A B +B C +A C =6(cm) B C D E P E : Q C =D P : B QÚ 8 :0=D P : 5 0D P =40 D P =4(cm) 4 MDP= MDC DPB= BCM A M =B M DPB=B M _P C _;!; DPB=4_5_;!; DPB=0(cm ) 5 6 _
ABC BAO= BCO BAO+ CBO= BCO+ CBO=90 6 ABE CDF BAE= DCF= x AEC AFC AEC AFC CAE= CAF BAE+ CAE+ CAF=90 x=90 x=0 7 E, F ABC, ADC ABC CDA ABCD= EPCQF_=60(cm ) 8 ABM= ACM=;!; ABC=0(cm ) A DÚ : D MÚ= : ADC: CDM= : CDM=;5#;_0=(cm ) 9 A DÚ G A GÚ : G DÚ= : G DÚ=x A GÚ=4x, A MÚ=A DÚ_;!;=6x_;!;=x EQ =6(cm) ABC E QÚ : B C = : 6:B C =: B C =9(cm) ABC MÚP =;!;_B C =4(cm) CDA P NÚ=;!;_A D =(cm) MÚNÚ=MÚP +P NÚ=7(cm) AMND MBCN AMND : MBCN =(6+7)_;!;_h : (7+8)_;!;_h = : 5 m=00 cm 0 cm 00 : 0=0 : 0 : =000 : 0 cm 000 4 A, B x : 00000=0 : x x=000000(cm)=0000(m)=0(km) = 555555555555555 ;6!0);=;6!; =0 MÚGÚ=x A MÚ : MÚGÚ : G DÚ = : : 0 A GÚ : G DÚ= : GE DF A EÚ : E F = : A EÚ=x E F =x BCE B DÚ : C DÚ=E F : C F = : A F : F C =(A E +E F ) : F C = : ABD E B : A B =E P : A DÚ : =E P : 6 E P =(cm) P QÚ =E P P Q =4(cm) _ 7
A - - BC =A B -A C =8-6 =8(cm) B C ='7cm - ABC D E =;!; A C =(cm) AE +CD =D E +AC =9+6 =45(cm) - ABC BC =DE =4(cm) C D +BE =DE +B C =4+6 =0(cm) -4 AB +CD =BC +AD AD =AB +CD -BC x =6+6-5=7 x= (cm) '7cm 45 cm 0 cm cm - - 5 cm, cm, cm =5 + - 0 > +5 9 <6 +7 = +5 0 =6 + 0 '5 <" + 0 DEC CE =CD -DE =5-6=9(cm) C E = cm B C =B EÚ+C EÚ =+=5(cm) 0 A C B D AD +BC =AB +CD x +y =5+6=6(cm) 5cm 6 cm -5 B P +D P =A P +C P B P +D P =9+6=5(cm) -6 P=R+Q=0+=(cm ) -7 ( + )+( + ) = + + ( + )= ABC 4 ;!;=6(cm ) 5 cm cm 6cm 04 B C M ABM A M =AB -B M =69-5=44 A MÚ=(cm) ABC=B C _A MÚ_;!; ABC=0 ;!;=60(cm ) 60 cm 05 x-, x-, x x x =(x-) +(x-) x =x -x++x -4x+4 x -6x+5=0, (x-5)(x-)=0 x=5 x= 8 _
x->0 x> x=5 5 A B =B C +A C x =8 +8 =8 x=8' (cm) A B =8' cm, A C =8 cm 06 ABC AB =AC +BC =6 +8 =00 AB =0(cm) ABDE=AB =00(cm ) 07 AB = +9 =5 A B =5(cm) AC = +6 =400 A C =0(cm) 00 cm A B =5 cm, A C =0 cm 08 a a >4 +6, a >5 a>'å a <4+6 a <0 'å<a<0 'å < a <0-4 ABD B=60 A B : B D : A D = : : =6:: A DÚ = (cm) ABC=;!;_B CÚ_A D =;!;_0_ ABC=5(cm ) -5 A(-, -), B(, ) A B = "{ -( -) } +{ - (-ç) } A B ="5 +çω A B = 5 cm -6 A(, -), B(x, 5) 0 0="( x- ) + (5+ ) Ω ="( x- ) + 6Ω 00=(x-) +6 00 =x -x++6 x -x-6=0, (x+7)(x-9)=0 x=-7 x=9-7, 9 - A - - x =5 + =4 x=å4 y =6 +6 =7 y=6' x=å4 - a S S= 55555555a =6 a =64 4 a=8(cm) - ABC A C =B C =8(cm) y=6' 8cm - EG =EF +FG =0 +6 =6 E G =å4 (cm) AG =AE +EG =8 +(å4) =00 A G =0' (cm) å4 cm 0' cm '6 - a 55555555a '6 55555555a= a=6'6 A B =6'6 (cm) a ABC 55555555a 4 ABC= 55555555_(6'6) =54 (cm ) 4 ' a 55555555a V-ABC ' 55555555_(6'6) =6 (cm ) 6'6 cm 54 cm 6 cm _ 9
- AO =AB -BO =00-6=64 A OÚ=8(cm) V V=;!;p_6 _8=96p(cm ) -4 r 0 p_6_ 55555555544 =pr r=(cm) 60 OAH OH =OA -AH =6 - = O HÚ=4' (cm) 6' V=;!;p_ _4'= 5555555555555 p(cm ) 96p`cm 6' 555555555555 p cm -5 E DÚ (-, 0), (9, 0) 0 ABH A=60 A B : A HÚ : B H = : : A B =4 cm A B : A H : B H =4 : : B H = (cm) 04 A B ="( -) + 6 ='4å5 A C ="8 +4 ='8å0 B C =" + (- )Ω ='ßå5 BC =AB +AC ABC (-, 0), (9, 0) cm ED =EH +DH =(5++5) + =48 E DÚ=å7 (cm) -6 A B'Ú r A A' =pr A A' =A B' -A'ÚB' =00-6=64 A A' =8(cm) pr=8 r=;ç$;(cm) å7 cm 05 a l l= a=8 a=8(cm) 06 BCD D E D E = 55555555a= 55555555_ D E =6 (cm) H BCD D HÚ=;@;_6=4 (cm) 8cm 4 cm ;ç$; cm 90 07 p 55555555544 =p_r 60 r=(cm) h=" - Ω h=" 5 ='å5(cm) 'å5 cm 0 B C =D C =8cm BD =BC +DC =64+64=8 B D =8' (cm) 0 x (k, 0) 'å0="( k- ) + (-ç) Ω ('å0) =(k-) +(-) k -6k-7=0, (k-9)(k+)=0 k=9 k=- 8' cm 08 B B'Ú ABB' A B =A B'Ú B= B'=60 ABB' B B'Ú=8(cm) 8 cm 0 _
B F A MÚ ABF= LBF EBC ABF E B =A B B C =B F EBC= ABF EBC ABF ABF= EBC E B D C EBA= EBC= ABF E B +A C EBC+ AEC BFML LBF= LFM AB : AC = : AB =x AC =x BC =AB +AC =x +(x) =0x B C ='å0x A C _A B _;!;=B C _A P _;!; x_x_;!;='å0 x_'å0_;!; 5 6 ABD A B =6 cm, A D =8 cm B DÚ=" 6 + 8Ω =0(cm) ABD A B _A D _;!;=B D _A HÚ_;!; 6_8_;!;=0_A HÚ_;!; A HÚ=4.8(cm) 4.8 cm A B ="( -4 +) +( - -5)Ω ="5Ω8 B C =" (+ 4) +( - +)Ω ="4Ω9 A C ="( + ) + (- -5)Ω ="6Ω5 AC <AB +BC ABC 7 ABP=A B _P Q _;!; ABP=_P Q _;!; ABP=6 P Q ACP=A C _P R _;!; x -0x=x(x-0)=0 x>0 x=0 A C =x=0(cm) 0 cm ADE AFE(SSS ) D E =E F E F =x cm E C =8-D E =8-x yy ABF A B =8 cm, A F =0 cm B F =" 0-8Ω =6(cm) F C =BC -BF =0-6=4(cm) yy EFC EF =FC +EC x =4 +(8-x) x=5 E F =5(cm) 5cm 8 ACP=_P R _;!; ACP=6 P R cm ABC 55555555_ =6(cm ) 4 6= ABP+ ACP =6 P Q +6 P R =6( P Q +P R ) PQ +P R =6 (cm) A G +A G =A G 6 cm 4 x cm x cm x =4 + =5 x=5(cm) 4cm 4 =x +, x =7 x='7(cm) '7 cm, 5 cm AG =AE +EG =0 +0 =500 A G =0'5 (cm) A G =0'5 (cm) 0'5 cm _
Æ Æ Æ Æ Æ B 0 - cos 60 tan 0 sin 60 ' =-_;!;_ 55555555_ 55555555 =-;4#;=;4!; ;4!; - - ABC AH =BH _CH =BH _9 BH =6(cm) AB =BH +AH AB =6 + =0 AB =0(cm) 0 cm 0 sin A=;!; A=0 cos A_tan A=cos 0 _tan 0 = 55555555_ 55555555=;!; sin A=;!; cos A= 55555555, tan A= 55555555 A / B C cos A tan A= 55555555_ 55555555=;!; ;!; BC BC - sin A= 45 =; ; cos B= 45 =; ; AB AB BC tan A= 45 =; ; AC ; ; ; ; ; ; - sin 0 +cos 60 -tan 0 =;!;+;!;-55555555 - sin 0 +cos 60 -tan 0 =- 55555555= 555555555555555 sin 60 +cos 0 +tan 60 = 55555555+ 55555555+ sin 60 +cos 0 +tan 60 = - 555555555555555-4 (tan 45 -sin 0 )_cos 60 ={-;!;}_;!;=;4!; sin 0 _cos 45 -cos 0 _sin 45 ' ' ' '6 '-'6 =;!;_ 55555555-55555555_ 55555555= 55555555-55555555= 555555555555555555 4 4 4 ;4!; 0 A AB : AC : BC : BC sin A= 5555555555 =;!7%; AB AC cos A= 5555555555 =; 7; AB BC tan A= 5555555555 =: 8 : AC '-'6 5555555555555555555 4 ;!7%; ; 7; : 8 : 04 BC =AB +AC, BC =6+9=5 BC =5 cm AB sin x=sin C sin C= 5555555555 =;5$; BC 05 sin A=;8{; A=0 sin 0 =;8{;, x=;!;_8=4 x=sin 0 _8 cos A=;8}; A=0 cos 0 =;8};, y= 55555555_8=4 y=cos 0 _8 06 tan 45 - cos 0 +' sin 45 =_-_ 55555555+'_ 55555555=;&; ' AB 07 cos A= 5555555555 =; 5; AC ; 5;=;5#; x=9 ;5$; x=4, y=4 ;&; 9 08 ABCª EBD A= E 'å0 sin A+cos E=sin E+cos E=;7#;+ 5555555555555 7 +'å0 sin A+cos E= 55555555555555555555 7 555555555555555555555 +'å0 7 _
Æ - AB AB - ABO sin a = 45 = 45 OA sin a =AB - 0 A 90 0 sin A, 0 cos A tan 45 = tan tan 46 > tan 46 AB x =45 x=5 04 COD CD CD tan a = 5555555555 = 5555555555 tan a =CD OD 05 tan A+tan (90 -A)=tan A+ 44444444 tan A sin A cos A sin A+cos A = 44444444+ 44444444= 44444444555555555555555555555 cos A sin A sin A cos A = 4444444455555555555555=5 sin A cos A 5 5 - cos (x -5 )=sin (x +45 ) x -5 +x +45 =90 x=0 tan x tan (x -0 )= x +(x -0 )=90 x=40-4 (sin A+cos A) ='5 sin A+ sin A cos A+cos A=5 sin Acos A= sin A cos A tan A= 44444444, 44444444= 44444444 cos A tan A sin A sin A cos A tan A+ 44444444= 44444444+ 44444444 tan A cos A sin A sin A+cos A tan A+ = 44444444555555555555555555555=;!; sin A cos A sin A 0 tan A= 44444444=sin A_ 44444444 cos A cos A tan A= 55555555_= 0 sin(90 -A)=cos A=; 7; BC =" 7-8Ω ="çω5 =5 tan A=: 8 : 0 x +x +45 =90 0 40 ;!; : 8 : sin A 06 sin A : cos A=4: 44444444=;$; cos A tan A=;$; AB ="4 ç+ Ω =5 cos A=;5#;, sin A=;5$; cos A-sin A={;5#;} -{;5$;} =-; 5; -; 5; 07 sin A+cos A='5 (sin A+cos A) ='5 sin A+ sin Acos A+cos A=5 sin Acos A= sin A+cos A 44444444+ 44444444= 44444444555555555555555555 sin A cos A sin A cos A + =(sin A+cos A)_ 4444444455555555555555 sin A cos A '5 + ='5_;!;= 55555555 08 +sin 0 =+cos 60 =(+cos 60 +sin 45 )(+cos 60 -sin 45 ) =(+cos 60 ) -(sin 45 ) ={+;!;} -{ 55555555} ' =;4(;-;!; =;4&; A 7 8 B C 5 '5 55555555 ;4&; _
=(sin A+cos A)= cos A x ADC tan 60 = 5555555555 AD Æ x=ad tan 60 AD ABD sin 45 = 5555555555 ' AD =_sin 45 =_ 55555555=' x=ad tan 60 ='_='6 '6 7 sin 0 =cos 60 cos 0 =sin 60 tan 0 _tan 60 = cos 60 sin 60 cos 0 tan 60 = 4444444455555555555555555555 + 44444444555555555555555555 sin 60 cos 60 =+cos 0 tan 45 =+_= cos 0 =sin 80 cos 0 <sin 8 <tan 45 sin 50 +cos 50 = sin 40 +cos 40 = cos 90 =0 sin 65 =cos (90-65 )=cos 5 cos 70 =sin 0 sin 0 >cos 70 8 9 (x +x+0 )+(4x+0 )=90 x +5x-50 =0, (x-5 )(x+0 )=0 x=5 0 <A<45 sin A<cos A "( sin A- cos ça )Ω =-(sin A-cos A) 5 4 5 tan A= tan A=;!; '5 sin A= 55555555= 55555555, '5 5 '5 cos A= 55555555= 5555555555 '5 5 '5 sin A+cos A= 5555555555 5 tan (x+5 )tan (x-5 )= x+5 +x-5 =90 x=0 4 sin xcos x=4 sin 0 cos 0 =4_;!;_ 55555555= 5 sin 40 =k sin 40 +cos 40 = cos 40 k +cos 40 =, cos 40 =-k 0 A 90 0 cos A O A 4 M 5 O' '5 5555555555 5 0 "( sin A- cos ça )Ω =-sin A+cos A "( sin A+ cos ça )Ω =sin A+cos A = cos A=, cos A= 55555555 A=0 tan 0 = 55555555= 55555555 4 sin A+4 cos A-5=0 sin A=-cos A 4(-cos A)+4 cos A-5=0 4-4 cos A+4 cos A-5=0 4 cos A-4 cos A+=0 ( cos A-) =0, cos A= cos A=;!; A=60 55555555 60 cos 40 =" -kω 6 sin A tan A= 44444444 cos A sin A -tan A sin Acos A=- 44444444_sin A_cos A cos A -tan A sin Acos A=-sin A=cos A (sin A-cos A) =sin A- sin Acos A+cos A (sin A+cos A) =sin A+ sin Acos A+cos A 4 _
Æ Æ B BCD DBC=45 BC BC cos 45 = 5555555555, BD = 5555555554455555 BD Æ cos 45 BD =' cm ' cm - BC - ABC tan 60 = 555555555, BC =_= BCD B=45 BC cos 45 = 5555555555, BD _ 55555555= BD ' BD =' ' AD - ABD sin 45 = 5555555555, AD =4'_ 55555555=4, AB ' BD cos 45 = 5555555555, BD =4'_ 55555555=4 AB ' AD ACD tan 60 = 5555555555, CD _=4 CD 4 CD = 55555555= 5555555555 4 +4 BC =BD +CD =4+ 5555555555= 55555555555555555555 0 ABC C +4 55555555555555555555 AB sin 60 = 5555555555, AB = 55555555_00=50 m BC 50 m 0 tan B=;!; B M =C M =AC =x ACM A M =AC +C M, 0 =x +x x =400 x=0' cm ABC AB =BC +AC =(0') +(0') AB =0'å0 cm BC 0 ABC tan 60 = 5555555555 AB BC =_tan 60 =_ = 0'å0 cm 04 BD =x CD =( +)-x ABD AD tan 60 = 5555555555, AD =tan 60 _BD yy BD Æ ACD AD tan 45 = 5555555555, AD =tan 45 _CD yy CD Æ tan 60 x=cd tan 45 x=( +)-x, ( +)x= + x= CD = cm ACD C= A=45 AD =CD =cm AC =AD +CD, AC =() +() =6 cm AC ='6 cm 05 ABH AH =AB _sin 60 =6_ 55555555= cm BH =AB _cos 60 =6_;!;= cm CH =BC -BH =7-=4 cm AHC AC =AH +CH =( ) +4 AC =7+6=4 AC ='4å cm '6 cm '4å cm 06 ABH AH =6_sin 60 =6_ 55555555= cm ACH A= C=45 AH =CH = cm AC =AH +CH =() +() AC =AH +CH =54 AC ='6 cm 07 BCH BH =CH ' BH =4_cos 45 =4_ 55555555=' cm ABH BH ' AH = 5555555554455555 = 5555555555555 =4'6 cm tan 45 '6 cm _ 5
AC =AH +CH =(4'6 +')cm (4'6 +')cm 08 ACH CH =x sin 60 = 55555555x AH =x cos 60 =;!;x BCH B= C=45 CH =BH AB =AH +BH =;!;x+ 55555555x=00 (+)x 55555555555555555555555 =00, (+)x=00 00 00 (-) x= 55555555555555= 55555555555555_ 55555555555555555555 + + (-) x=00(-) cm 00(-) cm - 0 - BC = 555555555445555555555555555555555555555 tan 60 -tan 0 BC _(tan 60 -tan 0 )=0 BC _{- 55555555}=0, BC _ 5555555555 =0 BC =0_ 5555555555 =5 cm 5 cm - ABC=;!;_6_0_sin(80 -x )=5 0 sin (80 -x )=5, sin (80 -x )=;!; 80 -x =0 x =50 50 - - ABCD=(AD +BC )_AH _;!; ABCD BH =6_cos 60 AD =BC -BH =0-_6_cos 60 =4 cm AH =6_sin 60 = cm ABCD=(4+0) ;!;= cm cm - ABCD=;!;_AC _BD _sin(80-0 ) ABCD=;!;_0 sin 60 ABCD=60_ 55555555=0 cm 0 cm 0 ABH h h BH = 555555555445555555, CH = 555555555445555555 tan 45 tan 0 BH +CH =0(cm) h h 555555555445555555+ 555555555445555555=0 tan 45 tan 0 h+ h=0 (+)h=0 0 0 (-) h= 555555555555555= 555555555555555_ 55555555555555555555 =5( -) cm + + (-) AH =5( -)(cm) 0 ABC=;!;_8_0_sin 0 ABC=40_;!;=0 cm 0 ABCD AD =BC =0(cm) ABCD=6_0_sin 60 ABCD=60_ 55555555=0 cm 04 ABCD= ABC ABCD=_{;!;_0_0_sin 45 } ABCD=400_ 55555555=00' cm ' 05 CH h AH =tan 60 _h, BH =tan 45 _h AH -BH =00 00 h= 44444444555555555555555555555555 tan 60 -tan 45 00 00 (+) h= 55555555555555= 55555555555555_ 55555555555555555555 - - (+) h=50(+) cm 5( -) cm 0 cm 0 cm 00' cm 50(+) cm 6 _
06 ABC=;!;_6_0_sin (80-50 ) ABC=0_sin 0 =5 cm 07 ABCD B=80 - C, B=80-5 =45 ABCD=8_6_sin 45 ABCD=4' cm 08 ABCD= ABD+ BCD ABCD 5 cm 4'cm =;!;_4_4_sin (80-0 )+;!;_8_5_sin 60 ABCD=4 +0 =4(cm ) BC sin 0 =;0H0; h=00_sin 0 =00 m ABCD B=80 - C=60 AB =CD =4 cm ABH AH =AB _sin 60 =4_ 55555555= (cm) 4 cm 00 m cm 5 6 ABCD ABP= ADP= BCP= CDP ABCD=4 ABP 0 sin 60 =4_ ABP ABP=45 cm 45 cm ABC B= C A=80 -_75 =0 ABC=;!;_0_0_sin 0 ABC=5(cm ) 5 cm 7 ABCD=(8+BC )_AH _;!; 8 AH =4' _sin 45 =4(cm) BH =4' _cos 45 =4(cm) BC =BH +HÚHÚ'+CH ' BC=BH +AD =6(cm) ABCD=(8+6)_4_;!;=48(cm ) 48 cm ABCD=;!;AC _BD _sin (80-50 ) ABCD=;!;_8_0_sin 0 ABCD=0(cm ) 0 cm ABC= ABD+ ADC ;!;_6_8_sin (80-0 ) =;!;_6_AD _sin 60 +;!;_8_AD _sin 60 ={ 5555555555 + } AD 4 7 = 5555555555 AD AD =: 7 :(cm) : 7 : cm ABD AD h CD =h (0+h) h=: h=0+h (-)h=0 0 (+) h= 555555555555555_ 55555555555555555555 =0( +)(cm) - (+) 0( +) cm - C - AOB : COD=μAB : μcd 0 : 60 =8 : μcd μcd =6(cm) - BCO BCO= BOC=x ABO CBO ABO= BCO+ BOC=x 6 cm _ 7
ABO O B =O AÚ ABO= BAO=x ACO AOC=90 ACO+ CAO=90, x =90 x=0 μae : μbd= AOE : BOD=90 : 0 = : : 0 O MÚ A B A MÚ=B MÚ A MÚ= cm OAM O AÚ =A MÚ +O MÚ x = +5 =69 x=(cm) cm - O MÚ A B A MÚ=B MÚ B MÚ=0(cm) O MÚ A B A B =A MÚ OAM A MÚ =O AÚ -O MÚ =5 - =6 A MÚ=4(cm) y=_a MÚ=_4=8(cm) x=0 cm, y=8 cm 0 xod =x-, OB =x DOB x =(x-) + x =x -4x+4+9 4x= x=: 4 :(cm) : 4 : cm -4 O MÚ=O NÚ A B =A C ABC A+ B+ C=50 + x=80 x=65 65 04 B D =B F =8 cm A F =A E C D =E C C D =A C -A E =A C -A F =7-=4(cm) B C =B D +C D =8+4=(cm) cm - - PTOT' P+ T+ O+ T'=60 75 +90 + x+90 =60 x=05 - A B +C D =A D +B C 7+=4+x x=6(cm) 05 6cm - l=" - ( 8-4 )Ω =" 4Ω 4-ç6 =" Ω8 l=8' (cm) 8' cm 05 O A B M OAM A=0 O AÚ : A MÚ : O MÚ = : : O AÚ =4cm O AÚ : A MÚ : O MÚ =4 : : A MÚ= (cm) A B =A MÚ=4(cm) 06 C D =C TÚ+D TÚ=A C +B D =(cm) C BD E A C =B E D E =B D -A C =9-4=5(cm) CDE C E =C D -D E = -5 =44 C E =(cm) A B =(cm) 4 cm cm 0 AOC AOC=60 BOC=0 μbc : μac= BOC : AOC= : μbc μac 07 ="çd - 6Ω, =d -6 d = +6 =44+56 =400 d=0(cm) 08 AB =" 0 -(5 +) =ß6=6(cm) 0 cm 6 cm 8 _
C - - x=;!; AOB=;!;_0 =5 y= AQB=_60 =0 z= ARB=_8 =56 5 0 56 - AM=μBM μam μbm APM= AQM= MQB AQB= AQM+ MQB=5 +5 =70 70 - BAC 90 BAT= BCA BCA+ ABC=90 70 + x=90 x=0 0-4 AOB μab AOB 60 BAT AOB x=60 60 0 AOB A O =B O AOB= P=00 x=(80 - AOB) =(80-00 ) =40 0 ABC= x AOC= x μac : μbc= : : BOC=4 x AOC+ BOC= x+4 x=80 6 x=80, x=0 OBC=0 0 BAT= PTA+ APT 70 = PTA+40 PTA=70-40 =0 ABT= PTA=0 04 ABC A B =A C BAC=0 ABC=75 ABCD ABC+ ADC=80 70 + x=80 x=05 05 90 μad=μde=μbe=μbc 40 0 0 05 μab ;!; 0 - A C ACF BAC=0, ACD=0, DCE=0 - ABCD BAD+ BCE+ DCE=80 AFE= BAC+ ACD+ DCE x=0 +0 +0 =90 90 00 + x+0 =80 x=50 50 06 B C ABC ACB 90 - ADB= ACB=60 (μab ) x= ADC= ADB+ BDC μac=μbd ABC= BAD= ADC=0 =60 +50 CAD+ BAD+ ABC=90 =0 x+0 +0 =90, x=0 0 CAD=0 0 _ 9
07 A B PAB P A =P B PAB=55 ACB= PAB=55 08 BOD μbd BOD= BAD= x ABCD BAD+ BCD= x+ x= x=80 x=60 BAD=60 55-6 P A P B =P T x_(x+6)=4, x +6x-6=0 (x-)(x+8)=0 x= x=-8 x>0 P A = cm cm -7 P A P B =P T O B =x 4_(4+x)=6, x=;%;(cm) O B =;%; cm ;%; cm 60 - - O AÚ=x O P =(x-) A P B P =(x-)_ C P D P =4_4 A P B P =C P D P (x-)_=6, x=5(cm) O AÚ=5(cm) - O D =x P C =O P -O C =0-x P D =P O +O D =0+x P A P B =P C P D 7_(7+5)=(0-x)(0+x) x =6, x=4(cm) - BAC= BDC x=50 ABD= ACD y=0 x=50-4 B+ D=80, x+95 =80 x=85 y= BAD=00 x=85-5 P AÚ P B =P C P D _6=x_4 x=(cm) P AÚ P D =P B P C _(+7)=_(+y) O D =4 cm y=(cm) cm 5cm 4cm y=0 y=00 cm 0 P A P B =P C P D P AÚ =x x =4_9=6, x=6(cm) P AÚ =6(cm) 0 C P D P AÚ P B =P C P D 8_8=4_P D, P D =6(cm) =P C +P D =4+6=0(cm) 0 ABCD P A P D = P B P C _(+5)=_(+x), x=0(cm) B C =0(cm) 04 P T =P A P B x =4_(4+0), x='å4 (cm) P TÚ='å4(cm) 05 B PÚ=D PÚ B PÚ=x B PÚ D P =A P C P, C P =A CÚ-P AÚ=8 cm B D =8(cm) x =_8, x=4(cm) 06 P C P DÚ=P AÚ P BÚ 5_(5+4)=x_(x+) 45=x +x, x +x-45=0 (x+5)(x-)=0 x= x=-5 x>0 x=(cm) P AÚ=(cm) 6cm 0 cm 0 cm 'å4 cm 8cm cm 40 _
07 C P =a O D =a P A P BÚ=P C P D B F =6 cm 6cm _4=a_(a+x)=a_a a =4, a=(cm) O DÚ=4(cm) 4cm 6 A P C P =B P D P 6_4=8_x x=(cm) D P = (cm) cm 08 P T =P A P B 6 =4_(4+x), x=5(cm) A BÚ=5(cm) μab 0 AOB=60 60 μab=p_6_ 55555555544 =p_6_;6!;=p(cm) 60 ABP APD= ABP+ PAB μbc PAB= PDC=65 APD=60 +65 =5 5cm p`cm 5 7 PQCD PQB D PQB= D=70 ABQP A+ PQB=80 x+70 =80, x=0 A=0 8 P TÚ =P AÚ P B P TÚ =_(+6)=6 P TÚ=4(cm) PBT B TÚ =P BÚ -P TÚ =(+6) -4, B TÚ =48 B TÚ =4 (cm) 0 4 cm 4 μqr QOR= QSR QOR=0 PQÍ, PRÍ OQP= ORP=90 60 P+ QOR=80 x+0 =80, x=70 P=70 70 CAB= CBT μab : μbc= : μab μbc : ACB : CAB= : 60 : CAB= : CAB=40 CBT= CAB=40 5 B FÚ=B DÚ=x A FÚ=A EÚ=4-x C D =C E =0-x A C =A E +C E =4-x+0-x = 4-x=, x=6(cm) 40 0 0 0 04 05 06 07 : 8 : cm 08 8'5 cm 09 0 6 cm 'ß5 4 ;!7^; 5 6 55555555 7 8 OD 9 'ß9 cm0 ;5@; 4 5 6 7 8-9 6 cm 0 cm 60 + 0 cm 4 56 cm +' 5 55555555555555555555 cm 6 : : cm 7 8 9 40 9cm 4 4 70 4 4p`cm 44 4.8 cm 45 cm 46 4`cm 47 8 cm 48 '5 0 ABD A B =B D +A D x =9 + =5 x=5(cm) ADC C A =A D +C D y = +6 =400 y=0(cm) x+y=5+0=5 (cm) _ 4
Æ ABC A=90 A D B C x =B D _B C =9_5=5 x=5(cm) y =C D _B C =6_5=400 y=0(cm) x+y=5+0=5(cm) 0 ABC C=90 B C =A B -A C =400-56=44 B C =(cm) C D =6(cm) C=90 ADC A D =A C +C D =56+6=9 A D ='7å (cm) 0 x x =6 +8 =00 x=0(cm) 8cm 8 =6 +x, x =8 x='7 (cm) A MÚ =A BÚ -B MÚ =6-6=0 A M ='5 (cm) ABC=B C _A MÚ_;!; ABC=8_'5_;!;=8'5 (cm ) 09 P O ="( x-0 ) +ç( - -0)Ω =" x +( -)Ω P O =x +4, ('å0) =x +4, x= 6 x=6 x=-6 0 a 55555555a 4 6= 55555555a a=(cm) 4 cm 55555555a 55555555_=6 (cm) 04 A C R B=90 ABC R=P+Q=8p+4.5p=.5p(cm ) AC x R=px _;!;=.5p x=5(cm) A C =5_=0(cm) 05 A B +C D =A D +B C 8 +6 =A D +7 A D =00-49=5 A D ='5å(cm) C D D E, B F A E B DÚ P P C =P E A P +P C A E A E =A F +E F =5 + =69 A E =(cm) 06 E D =;!;B C =5 A=90 B C E D B C +E D =B E +C D B E +C D =0 +5 =5 07 E C =A C =x C DÚ=E D -E C =4-x ACD D=90 A C =C D +A D x =(4-x) + 08 ABC A B C M B MÚ=C MÚ x=: 8 :(cm) ACB= ECD=60 ACE=60 ACH C=60 A C : C H :A H = : : =6:: ACE=C E _A H _;!; ACE=8 ;!;= (cm ) BC tan A= 5555555555 =, BC =AB _= AB AC =AB +BC =() +() =5 AC ='å5 4 ABC BC =AB +AC =8 +5 =89 BC =7 cm 4 _
ACB=x ABC=y sin x =sin C=; 7;, cos y =cos B=; 7; sin x +cos y =;!7^; 5 sin 0 =0, cos 90 =0 sin 0 +cos 90 =0 6 cos 0 =sin 60 =sin 60 _(sin 5 +cos 5 ) =sin 60 _= 55555555 7 cos 0 =sin (x+y) 0 +x+y=90 x+y=60 yy tan (x+y)tan (x+y+0 )= x+y+x+y+0 =90 x+y=80 yy - x=0 x=0 x=0 y=5 y-x=5-0 =5 =(tan _tan 89 )_(tan _tan 88 ) =_y_(tan 44 _tan 46 )_tan 45 =_tan 45 = (sin A+cos A) ={ 55555555} '5 sin A+sin Acos A+cos A=;5(; sin A cos A=;5(;-=;5$; sin A cos A=;5@; 0 <A<45 sin A<cos A " sin A- cos ça )Ω =-(sin A-cos A) " sin A- cos ça )Ω =-sin A+cos A " sin A+ cos ça )Ω =sin A+cos A =-sin A+cos A-(sin A+cos A) =- sin A sin A cos A sin A+cos A 4 = 555555555555555+ 555555555555555= 5555555555555555555555555555555555 cos A sin A cos A sin A = 5555555555555555555555555555 cos A sin A 8 OCD AD OD cos x = 5555555555 = 5555555555 =OD OC Æ 9 BC D E BCD=0 DCE=60 DE =4_sin 60 = cm CE =4_cos 60 = cm BED BE =BC +CE =6+=8 cm DE = cm BD =BE +DE =8 +() BD =BE +DE =64+=76 BD ='å9 cm 4cm B A 0 6cm D 4cm 60 C E sin A-cos A=;5!; (sin A-cos A) ={;5!;} - sin Acos A=; 5; sin A cos A=-; 5;=;@5$; sin A cos A=;!5@; tan A+tan (90 -A)= 5555555555555555555555555555 =;@%; cos A sin A 5 ADC AD =a CD CD cos 0 = 5555555555 = 5555555555 AD a CD =cos 0 _a= 55555555a (+) BC =BD +CD =a+ 55555555a= 5555555555555555555 a +cos x-+cos x cos x 0 = 5555555555555555555555555555555555555555555555 = 5555555555555555555 -cos x sin x sin x=cos x cos x cos x 5555555555555555555 = 5555555555555555555 = sin x cos x 6 A= BAC+ CAH A=5 +45 =60 BH BH tan 60 = 5555555555 = 5555555555 AH 00 BH =00_tan 60 =00 _ 4
Æ Æ BC =BH -CH =00-00 BC =BH -CH =00(-) m 7 tan(x+0 )tan(x+0 )= x+0 +x+0 =90 x=60 x=0 ODC OC =8_cos 0 =4 cm OCB OB =4_cos 0 =6 cm OBA OA =6_cos 0 = cm 8 x +x+k=0 - (cos 0 -sin 0 )={ 555555555555555 }=- a - ( -)+a=- a=-- k ( -)(--)=k 9 ABD BD =AD =8 cm k=- B=x B+ BAC=x=90 B= BAD= CAD=0 ACD AC cos 0 = 5555555555, cos 0 _AD =AC AD AC =8_ 55555555=4 cm ABD=BD _AC _;!;=8_4_;!; ABD=6(cm ) 0 C AB H ACH A CH sin 45 = 5555555555 AC CH =sin 45 _AC = 55555555_6'=6 cm ' CBH BCH= ACB- ACH CBH BCH=05-45 =60 CH cos 60 = 5555555555, CH =cos 60 _BC BC 6=;!;_BC BC = cm f x =cos x+sin x+5 f x =cos x+-cos x+5 f x =-cos x+cos x+6 f x =-{cos x-cos x+;4!;-;4!;}+6 f x =-{cos x-;!;} +;4!;+6 f x =-{cos x-;!;} +: 4 : cos x=;!; : 4 : x=60 ABD ABD+ BAD=0 AD =BD ABD= BAD=5 ADC ADC=0 CAD=60 AD =BD =a AC =;!;a CD = 55555555a BC tan 75 = 5555555555 =BC _ 5555555555 AC AC (+)a tan 75 = 55555555555555555555555 _;a@; tan 75 =+ AE BD ABD= EBD ABCD= BCD+ ABD ABCD= BCD+ EBD ABCD= BCE ABCD=;!;_8_0_sin 60 ABCD=;!;_40 cm =0 cm 4 D BC E BH cos 60 = 5555555555, BH =cos 60 _AB =4(cm) AB HE =AD =0(cm), CE =BH =4(cm) AH sin 60 = 5555555555, sin60 _AB =AH AB AH =4 (cm) ABCD (0+8)_4 55555555555555555555555555555555555 =56 cm CH 5 ACH sin A= 5555555555, AC CH =sin A_AC CH = 55555555_= cm CH BCH sin B= 5555555555, BC CH =sin B_BC = 55555555_BC BC = cm ACH AH =AC -CH AH = cm BCH BH =BC -CH BH ='6 cm 44 _
ABC=AB _CH _;!;=(AH +BH )_CH _;!; +' ABC=(+'6) ;!;= 555555555555555555555 cm 6 ABC=;!; ABCD, ABM=;!; ABC ABM=;4!; ABCD=;4!;_0_6 sin 60 ABM=: : cm 7 μbc BOC μbc BOC=40 AOC= BOC- AOB=60 ADC μac AOC ;!; ADC=0 8 O PQ R P E =P R, D Q =Q R CPQ CP +PQ +QC =C P +P R +Q R +C Q CP +PQ +QC =C P +P E +C Q +DQ CP +PQ +QC =C E +C D =C E (A C +B C -A B ) (+-5) C E = 555555555555555555555555555555555555555 = 55555555555555555555555555555555 C E=5(cm) CPQ 0 cm 9 A, B, C ABC A B =A C +B C =6+64=00 A B =0(cm) pr=p_5=0p(cm) 40 P A P B =P TÚ P TÚ =P C P D P A P B =P C P D 4_9=_(+C D ) C D =9(cm) 4 80 4 A D APD APC= BAD+ ADC μbd ;6!; a=80 _;6!;=0 μac : μbd=4 : b : a=4 : b=;$; a=40 APC= a+ b=70 4 BAC= BPC- ACD BAC=85-5 =60 μbc=8pcm 60 x 60 :8p=80 : x 60 x=80 _8p x=4p(cm) 44 AOO' ;!;_5_A M =;!; 4 5A M = A M =.4 AB =_A M =_.4=4.8 45 4+9=(cm) T T ' =" - (9-ç4)Ω ="çω4ω4 = T T ' =(cm) 46 T T ' =" 6 - (6+ç4)Ω ="5 7Ω6=4 T T ' =4(cm) 47 ACF A CÚ =A BÚ +B CÚ =6+6= A C =4'(cm) 55555555_(4') =8 (cm ) 4 48 A C ABCD a A CÚ =A BÚ +B CÚ =a A H A H =A E +(E F +F G +G HÚ) =a +(a) =0a A H ='å0 a 'å0 a='5 _'a A C =' a '5 O A 4 M 5 O' _ 45