중등수학2팀-지도서7

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2 3 6~7 8~3 3 ª 33~ ~39 40~ ~ ~ ~6 6~63 64 VII.

3 4 9 (Klein F849~95) (rlangen Program) (group of transformation) ' O' =k O ' O k O ' O ' O ' ' ' '

4 (topology) = = O O' =k O ' ' ' O O' O' O' = = =k O O O ' (000) 8 Howard ves (997) (99) VII.

5 600 (Thales ;?.. 640~?.. 546)

6 x 4x=6 34=5x 3 x x4=..4 = 4 8 = = F 4 8 a 4 8_a=8a 4 8a =4a a4a=4 8 4 lm a l ab 0 m b (S ) F F (S ) a=0 b=75 VII.

7 0 0. ª 0 0

8 ª similis s 7 (Leibniz G W 646~76) ªFGH F G H F FG GH H F G H mn mn n m =H=0 I==95 FG =63= GH = GH = = _4= (cm) 3 '' =3 5'' =3 '' =5 cm 3 '' =3 =3 =4 cm VII.

9 '' =68=34 34 '''' '' =34 3x=34 x=4 '' =34 6y=34 y=8 '' =34 5z=34 z=0 F O O O =O O =O FO = G F O H H =69=3 3 8GH =3 GH = cm =F=80 3 F O F

10 0. = F = F = (SSS ) (SSS ) (SS) (SS ) ( ) (S ) VII.

11 80 NO = NM =45=N=60 ªNOM (SS ) =R=50 F=P=90 FªQRP ( ) GH LJ =HI JK =IG KL =3 GHIªLJK (SSS ) aa'=bb'=cc' abc=a'b'c' ' b c' b' c ' ' a a' ª (SS ) =36= x = x0= x=5 ª (SS ) =47= x = x5= x=0

12 = ª ( ) OªO ( ) O O = 46=6x x=9 ª ( ) = 64=(4+x)6 x=5 ª = 08=8x 3 x= 5 ª = 0x=59 x= ªH H = 84=(4+H )8 H = cm 3 ª ( ) = 69= 6 =4 cm VII.

13 90 m n a l l' a a l=pm_ l'=pn_ a a ll'=pm_ pn_ =mn

14 = ª ( ) = (5+x)4=05 x=3 =64=3 =96=3 ª (SS ) =3 8x=3 x= (6+x)=3 x= 4.5(4.5+y)=3 y=9 ==90 ª ( ) = x=8x x =6=4 x=4 '' =56 56 H 'H' =56 H =F =0 cm 0'H' =56 'H' = cm c b z x y a ª = cx=ac c =ax ª = by=ab b =ay ª = zy=xz z =xy VII.

15 0 0. = ª ( ) ª = =86=43 = =86=43

16 = = x8=96 x= 96=5y y=0 = = 05=8x x=4 05=0y y=5 == = = =8 cm = + =6+8=4 (cm) =x cm = (4+x)4=46 x= = + =4+ = (cm) 3 3 = F ª = yy = F= = = yy = F F =F yy F =F yy ªF = F F = = VII.

(4+x)4=46 x= 6 3 6 8 = + =4+ = (cm) 3 3 = F ª

17 = () ª (SS ) = = 4=3x x=6 =4 = 40=x x= 4 5 P P =4.53=3 R R =64=3 P P =R R PR P P =34.5=3 Q Q =.55= P P +Q Q PQ Q Q +R R QR ab=cd=ef bb'=dd'. ab=cd bb'=dd'. km 3. km km a km a km.3.=a a b' e b f d d' c

18 3x=48 x=6 8x=(9-4)4 x= 3 5 a b c d l m mm' pp'=qq'=rr' a b c d l m p' p q' q rr' m' p q r a g h l m n g l h F m G m G F G F n F =G GF yy F G G GF = F yy = F = F = (6+x)6=00 x=6 = 8x=(5-0)0 x=6 43=8x x=6 4(4+3)=y4 y=8 55=x6 x=8 y=55 y=4 3 a R a Q a P X X P =PQ =QR =a P Q R R P R Q R X VII.

19 0.

20 MN = =PQ =5 (cm) LM = = _0=5 (cm) LN = = _6=8 (cm) MN = = _4=7 (cm) LMN =LM +LN +MN =0 (cm) 4 F = = H = = HH' 4 H H' F Q Q Q (S ) Q Q =Q Q = Q PQ PQ = = ( + ) Q Q = PQ = P ( + ) PQ = ( + )= (5+9)=7 (cm) Q VII.

21 M =M MP = M = M P =P yy N =N NQ Q =Q yy P Q PMN N N =N yy N MN M (S ) N = yy N M NP = = NP = MP = NP =MP PMN PM =PN = = + M P N Q P Q N M P Q MN = = MN =_8=6 (cm) x=6 N =N N = = _=6 (cm) y=6

22 G G G = G 3= G =6 cm =G +G =6+3=9 (cm) G = = =_8=6 (cm) G G = G = = _=8 (cm) 3 3 G G = G 5= G =0 cm F G 3 3 GF = GM GM = GF = _4=6 (cm) 3 G GM = M M =3 GM =3_6=8 (cm) 3 VII.

23 G=S G=S G=S S =S =S = 3 G S S S GF=S GF=S G=S G=S G=S G=S S S F G S S S S S =S =S =S =S =S = 6 =6G=6_8=48 (cm ) GF=G+FG = = _48=6 (cm ) 3 3 O =O O =O O = = _4= (cm) P P PO = PO = O = _=4 (cm) 3 3 M + =(M +M ) = + = +(M +M ) = +M +M M +M yy M = + = +(M -M ) = +M -M M +M yy + + =( +M )+ M =(M +M ) + =(M +M ) = = _0=5 (cm) x=5 = =6 cm x=6 M= = _48=4 (cm ) N= M= _4= (cm ) 3 G GM = 8GM = GM =4 cm M M M M =M =M =M =(G +GM )=_=4 (cm)

24 =3 p_0 =00p`(cm ) p_5 =5p`(cm ) 00p5p= = 3 VII.

25 ma mn (ma) (na) =m a n a =m n mh ma ma nh na na na (ma)(mh) (na)(nh) = m ah n ah=m n ma mb (ma)(mb)(na)(nb) =m abn ab=m n ma na na p(ma) p(na) =pa m pa n =m n O O' 3cm 5cm 36= O O' =4 nb OªO ( ) 3 3 =49 40O=49 O=90 cm 46= _p_4 = p`(cm ) _p_6 =88p`(cm ) p88p= = 3

26 mn m n 95= =95 S 95=80pS S=500p`cm 0 cm cm 0=5 5 =5 0 cm cm 5 mn na ma mc nc ma na mb nb ma na ma na (ma) (na) =m n (ma)(mb)(mc)(na)(nb)(nc) =m n mh ma na nh na ma 4 4 p(ma) (mh) p(na) (nh) p(ma) p(na) =m n =m n m.5 m 3m ª ( ) = 4.5.5= =3 m 3m VII.

27 ' ' 4.8 cm 7. cm 65 ' '' =000 =000 '' =000_6.6=6600 (cm)=66 (m) =764 V 764=8V V=9 cm ª ( ) =3 = =95 =95 7=95 =75 3 r _r=r _r=4r rr4r=4 4 = =764 7(64-7)= x 737=08x x= cm cm 6 cm cm 3cm km

28 O O O O O O O' ''' O ''' O =' O O' = VII.

29 m n m n = l m a a' b b' lmn ab=a'b' n O G = G I

30 km 6=y3 y=9 mn 6x=99 x=6 F = ( + )= (5+7)=6 (cm) =4 3 3 =7 8cm V 7=8V V=6 cm P = QP 84=x x=6 P = Q 84=0y y=5 M N MN P P =N N = P =P P =x cm G =P -=x- (cm) G G G = (x+)(x-)= (x-)=x+ x=6 P 6cm 49= =87 VII.

31 0 O = O = O O = F (F )( )= 40x= x=80 80 cm 0 ª ( ) = 8(5+ )=58 = 39 5 cm 04 ª ( ) = = 8 =6=4 =4 cm 03 ªF ( ) F =(6-x) cm = F 66=6(6-x) x=0

32 G F =G F 3=G 6 G =4 cm G G = G 4= G =8 cm 05 PQ P P = P =PQ PªP ( ) P P = =8=3 P P =3 P =5 PQ PQªP ( ) P =PQ 5=PQ 8 PQ = cm G G GF = G F =3 07 ªPQª mn m n P Q PQ ªPQª ( ) PQ PQ= =4 PQ PQ=(4-)=3 7=3 =9 cm PQ=+PQ=9+7=36 (cm ) PQ 3 PQ= 3 =49 PQPQ=4(9-4)=45 36PQ=45 PQ=45 cm 08 mn m n =95 36 L S L 95=36S S=00 00 L VII.

33 849 Mathematicschennalen ncyklopḣa die

34 0 05 8cm 6cm 6 cm 0 FGH 35 FGH 6cm F 5 cm G H 06 =4 cm =6 cm =8 cm P 4cm P 8cm 6cm 03 IJ x+y I L x cm F 0 cm H 8cm G J N K 5 cm M P y cm O 6 cm 07 =90 H H +H 3cm H 5cm 04 x x cm 8cm 8cm 4cm cm 6cm 08 x 4cm x cm 6cm 9cm VII.

35 09 pqrs 4x+5y-z p 5 q x 6 8 y 6 r z 8 s 3 M N P Q PQ =8 cm x+y 30 P 0 x cm Q M 8 cm N y 0 l m y=- l m (-3 4) =3 l a =b ab (-3, 4) l m y O x y=- 4 6cm M F N M N M =F =6 cm F F 4cm 5cm 8cm cm F 5 G G = cm G cm F ªF F =47 F = 36 7 cm 9cm F ª F =34 cm 6 G G' G G GG' G'M G G' M

36 7 G G =54 cm GF F G 600 9cm 6cm 8 =8 cm 00 cm 0 cm 0 cm 30 cm 40 cm 3cm 5cm 60 cm 80 m 6 F=6 =90 F =0 cm F =5 cm 80 m 5cm 60 cm 6 0 cm F cm 50 cm 00 cm 50 cm 00 cm 50 cm 3 0 cm 9cm cm 3 9cm 3 7p cm 76p cm 80p cm 84p cm 88p cm 4 3m 8m 0 m 6 VII.

37 80 cm 6 6 4cm 48 cm cm cm 9 48 cm 8cm 6cm m 7.5 m GH =6GH =35 GH =0 cm FG = 5=35 =9 cm FGJ (9+6)+(5+0)=80 (cm) 03 H LP =05=3 FG NO =x6=3 x=4 GH OP =8y=3 y= x+y=4+= =PQ 6 PQ = cm 5 48 P= _8_ = (cm ) 5 5 =H _ 9 3 =H _5 H = cm 5 H =H _H H = _{5- }= _ ={ } H = 5 cm 9 H +H = + = (cm) = x4=96 x=6 58=x6 5 x= 4 58=6y 48 y= 5 6z=88 z=6 4x+5y-z=5+48-6= = = ª (SS ) = x8= x=6 ==90 ª ( ) = ( +8)6=68 =4 cm PP ( ) P P =46=3 P Q P =PQ 4cm P Q 8cm 6cm 0 (-3 0) =4 =6 (y ) 4 a= = = (x ) 3 x y=- = 46=3b b= 4 9 ab= _ =6 3 F P P =x cm FP =y cm =P 49=x x= cm 4cm x cm y cm F P 5cm cm

38 F =FP 59=y8 y= F =x+y= + = (cm) F= = _54=7 (cm ) F= F= _7=8 (cm ) 3 3 GF= F= _8=6 (cm ) F =37 = PQ =_8=6 (cm) PQ PQ=y y=80 -(30 +0 )=40 y=40 8 =83 =8 3 =649 8=649 =8 cm =- =8-8=0 (cm ) MN = = _6=8 (cm) x=8 x+y=8+40= = =85 V 4 85=6V V=50 cm 5 M = = _6=3 (cm) F =3 cm =MF =_(3+3)= (cm) G F G F =3 G F =G F 3=G 6 G =4 cm G =4 cm =G +G =4+4=8 (cm) G 6cm F 6cm = = { _p_9 _}_ =84p`(cm ) =3 3 =87 x 87=600x x= G GM = G = 3 M = F 0.05=800. =40 m GG' G'M = =40+.6=4.6 (m) GG' = GM = _ M = M G'M = GM = _ M = M G GG' G'M = M M M =6 3 4 ª ( ) = 3=08 =7.5 m = =88 VII.

Áß2±âÇØ(01~56)

Áß2±âÇØ(01~56) PRT 0 heck x=7y=0 x=0y=90 9 RH RHS 8 O =8 cmp =6 cm 6 70 7 8 0 0 0 SS 90 0 0 0 06 07 08 09 0 cm 6 7 8 9 0 S 6 7 8 9 0 8cm 6 9cm 7 8 9 cm 0 cm x=0 y=00 0 6 7 9 8 9 0 0 cm 6 7 8 9 60 6 6 6 6 6 6 7 8 7 0