Dy hc kin toCu hi: Tm cc v d minh ha qua dy hc cc tnh hung in hnh (dy hc khinim !nh "# quy t$c gi%i &'i t()* t+,ng ch-.ng t+nh T/0T ch, cc n1ng "2c ki3n t,ki4n th5c v' cc &in )h) +6n "uyn n1ng "2c ki4n t, ch, /78 Nng lc kin to kin thc:9:1ng "2c d2 ,n )ht hin v;n < )h-.ng )h) d2a t+3n c. => cc quy "u(t t- duy &in ch5ng t- duy ",gic kh% n1ng "i3n t->ng v' di chyn cc "i3n t->ng8? c@ n1ng "2c d2 ,n )ht hin v' gi%i quy4t v;n < hc =inh cAn -Bc +6n "uyn ccn1ng "2c th'nh t nh-: n1ng "2c CDm CEt cc i t-Bng t,n hc cc quan h t,n hc t+,ng mi quan h giFa ci chung v' ci +i3ngG hc =inh cAn n$m mi quan h nhn qu%cAn c@ n1ng "2c =, =nh )hn tch tHng hB) Ic &it h@a tHng qut h@a n1ng "2c "i3n t->ng cc i t-Bng quan h J &i4t vKi cc i t-Bng t-.ng t2 quan h t-.ng t28VD1: 9 Li4n th5c kinh nghim J c@:Ch, hnh &nh h'nh MNCO8 Ta c@( )P P P PP AC BD AB AD + +Th(t v(y:( )P P P P PPP P P PP P P P( * (Q*(P*(Q* (P*: P( *AC AH HC h b xBD BK KD h b xAC BD a b + + + + + + + +9 Tnh hung: Tnh R d'i -Sng t+ung tuy4n tam gic MNC8( )P P P PQP PTam b c a + 9 Ui%i quy4t v;n 8(Q* t+> th'nh: PP l _QT T Q _P l _tt t ttt

>+ + + > ( )( )PP l P l P l P l P l Q PPxxxt x ( )( )PP l P l P l P l P l Q PPxxxt x + + + `(y )h-.ng t+nh J ch, c@ hai nghim "'P P x x 89 :1ng "2c huy Rng ki4n th5c gi%i quy4t cc v;n < t,n hc8 Cc th'nh t cVa n1ng"2c n'y chV y4u "':] :1ng "2c "2a chn cc cWng c thch hB) gi%i quy4t mRt v;n th'nh &;t bng th5c vEc t. n',o ( )8 8 ' ! ' ! r r r rCch l: Ta c,i( )PP P P P P aax b& B b A x & C + + + &;t bng th5c t+> th'nh:P_ B AC 8 `4 t+i cVa &;t bng th5c gBi ch, ta ing nng v4 )h%i "3n &(c T t -Bc mRt =2 cn &^ng t+,ng )h-.ng t+nh chbng hn nhn (Q* nh- "'P P P* c,= (=in x x + ta c@:( )T T T T P PP PQ =in c,= =in c,= P=in c,=P=in c,= _x x x x x xx x + + + C*ch E: :hn )h-.ng t+nh J ch, nh- "' mRt )h-.ng t+nh ch5a nhi th'nh h: P Pl l Q lT _ P u P l _D P P D D DP P D P D D ' ' ' ' Chx c@l_DP 'tha k8`Ki l_DP ' th u v "' nghim cVa )h-.ng t+nh: P_l _ltt tt Lhi @ ta c@: l _m l lml lm _xx xxxx+

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+ ' `(y )h-.ng t+nh J ch, c@ nghiml x h,Icm x Cch P: ?Itl m _ t x x + + ( ) ( )( ) ( )PPu P l 8 mul 8 mPt x xtx x + + + (Q* t+> th'nh )h-.ng t+nh thD, &i4n tPPQul P l _l Pttt t tt Ta nh(nl l m l t x x + + kl m x 8 Nnh )h-.ng hai v4 cVa )h-.ngt+nh ta -Bc:( ) ( )ll 8 m _mxx xx + `(y )h-.ng t+nh J ch, c@ nghiml x h,Icm x 8VD4: Cho hnh 6Vp phng ABCD3WUGH c9nh a3 HX& x*c $+nh !. tRnh $Q d.i $7ng!'Png gOc ch'ng c-a AH !. DB3 Cch Q: 0h-.ng )h) tHng hB)T+3n hnh &3n M AH @ DB \: "' -Sng vuWng g@c chung cVa M/ v' ON8 Tf \kyMP AD ( P AD * th( ) MP ABCD v'P@ DB ( thD, !nh "# &a -Sng vuWngg@c*8 T-.ng t2 ky :{MO ({MO* th :{(MO/* v' {\M/8 /ai tam gicM\{v' O:0vuWng cn n3n O{ {: {0 0\ 0Mla 8 }i c@ PlaP@ PPP P PP ll l la a aM@ MP P@ M@ _ _ + + , ,.Cch Cc !nh v! t+ cVa im \ v' : =uy +a hai im 0 v' { chia ,n OM th'nh &a)hAn &^ng nhau8Cch P: 0h-.ng )h) vDc t.: };y M "'m gc v' &a vEc t. c. => "'( ) ( )

AD a AB b AW c a b c a AH a cAM 0 AH 0 a c DB b a D@ mDB m b a + + uuur uruuur r uuur r r r r uuur r ruuuur uuur r r uuur r r uuur uuur r r( ) ( )( ) Q M@ A@ AM AD D@ AM a m b a 0 a c m 0 a mb 0c + + + + uuuur uuur uuuur uuur uuur uuuur r r r r r r r r 8`8 _ M@ DB uuuur uuur r n3n:( )( ) ( )( ) ( )P PQ 8 Q _ P Q _ Q m 0 a mb 0c b a ma 0 m a m 0 + + + r r r r r `8 _ M@ AH uuuur uuur r n3n:( )( ) ( )( ) Q 8 Q P _ P m 0 a mb 0c a c m 0 + + r r r r rTf (Q* v' (P* ta thu -Bc lQ 0 m8O, @ PPQ Q Q l

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l lAM AH D@ DB uuuur uuur uuur uuur ta Cc!nh -Bc v! t+ cc im \ :8Cch l: 0h-.ng )h) ta R};y gc tam din vuWng xnh M cVa hnh "() )h-.ng "'m h t+2c chukn MCy8 Cc xnhO N "An "-Bt n^m t+3n MC My M8 O d tnh t,n ta ";y cnh hnh "() )h-.ng "'Q a 8Ta R cc xnh:( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) M _G _G _O QG _G _N _GQG _ _G _GQC QGQG _U QGQGQ _GQGQ/ QG _GQ8 `(QG _GQ* AH uuurn3n )h-.ng t+nh dng tham = cVa M/ "': QQQ_x t& tY t 'Ta "i c@ ( QG _GQ* DB uuur n3n )h-.ng t+nh dng tham = cVa M/ "': PP PQ

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_ GlQGlP@ Q Q QG Gl l lM@ _ ,uuuur lPM@ uuuur (khi a Q*8`(y vKi a thy # th Pl aM@ 8- BP4: ThWng qua dy hc cc tnh hung in hnh che t+ng c'i It thch hB)cch "uyn t() thch hB) ch, hc =inh cc quan im &in ch5ng cVa t- duy t,nhc8 CAn che t+ng ch, hc =inh cc mi "i3n h giFa ci chung v' ci +i3ngquan h giFa ci c th v' t+fu t-Bng CDm CEt =2 v(t t+,ng t+ng thi v(n Rng&i4n Hi8VD1: Oy hc !nh " h'm =in (//Q_*9 Tnh hung: Tm mi "i3n h giFa cnh v' g@c vKi &n knh t+,ng tam gic89 pEt cc t+-Sng hB) Ic &it cVa tam gic MNC8a* Tam gic MNC vuWng ti M&* Tam gic MNC cn ti M v' g@c M &^ng _QP_ 8c* Tam gic MNC