DREPTE I PLANE CLASA A- VIII- A Ș OLI MPI ADE FI E 8 Ș 1) Segmentele [AB] şi [CD] !nt it!"te #e $%e#te ne&'#l"n"%e( M ete mil'&!l Segment!l!i [AB]( i"% N ∈ [CD] "t*el +n&,t CN .ND/ N't0m &! ( 2( 3( T #!n&tele ∈ [CM] &! .M C( 2 ∈ [AN] &! AN 4A2( 3 ∈ [MD] &! M3 .3D( T ∈ [BN] &! BN 4BT/ 5!ti*i&"6i &'#l"n"%it"te" #!n&tel'% ( 2( 3 şi T/ OL SAT 7 MARE 41 4) T%i!ng9i !l ABC $%e#t!ng9i& i'&el &! ( ) 8 :8 = A m "%e ;,%*!l A it!"t +nt%-!n #l"n α / AB şi AC *'%me"<0 &! #l"n!l α !ng9i!%i $e "&ee"şi m0!%0 u / Fie = = ( C B #%'ie&6iile ;,%*!%il'% B ( %e#e&ti; C #e #l"n!l α / ") Dem'nt%"6i &0 BC C B / >) Dete%min"6i inte%;"l!l +n &"%e e "*l0 m0!%" u / .) Pe #l" n!l t%" #e< !l!i i' &e l '%t '$i "g'n "l( !n$e CD AB ( cm CD cm AB ? ( 18 = = ( e %i$i&0 #e%#en$i&!l"%" { } ( ) O AC BD OP = ∩ ( ( cm OP @ = / A*l"6i ") Dit"n6" $e l" #!n&t!l P l" $%e"#t" ( ) AB DM DM ⊥ ( / >) Dit"n6" $e l" O l" #l"n!l ( ) PDA / OL SIBI7 41 OL ARAD 411 ) Fie t%"#e<!l A BCD şi $%e#t!ng9i!l BDEF it!"te +n #l"ne #e%#en$i&!l"%e/ D"&0 AB 4DC( BD 14&m( { } AC BD O ∩ = şi ( ) 8 ?8 m AOD ∠ = 0 e $ete% mine l!ngime" #%'ie&6iei egment!l!i [EF] #e $%e"#t" AC/ ?) Fie ABCD !n $%e#t!ng9i &! AB1? &m( AD14 &m( AE ⊥ BD( E ∈ DC)/ Pe #l"n!l $%e#t!ng9i!l!i e %i$i&0 +n E #e%#en$i&!l"%" #e &"%e e i" #!n&t!l F ( "t*el + n&,t FE(@ &m/ ") Dete%min"6i m0!%" !ng9i!l!i *'%m"t $e #l"nele FBD) şi ABC) >) Dete%min"6i $it"n6" $e l" #!n&t !l A l" #l"n!l FBE)/ OL VASL7I 41 ) Fie t%i!ng9i!l i'&el ABC( AB AC1. &m( BC1 &m i AM ⊥ ABC) &! AM 14 . &m/ Se &e%e ") $i t"" $e l" M l" B C >) $it" n " $e l" A l" MCB) ț &) m0!%" !ng9i!l!i $ie$%! *'%m"t $e #l"nele ABC) i MBC)/ ș 8) Se &'ni$e%0 #0t%"t!l A BCD şi #!n&t!l S ete%i'% #l"n!l!i 0! "ş" +n&,t SASB SCSD/ D"&0 AB14 &m( AP ⊥ CS( P ∈ SC) şi APSO( !n$e O ete &ent%!l #0t%"t!l!i( e &e%e ") M0!%" !ng9i!l!i *'%m"t $e $%e#tel e SC şi BD >) Dit"n6" $e l" #!n&t!l A l" #l"n!l BPD) &) Dit"n6" $e l" #!n&t !l B l" $%e"#t" $e int e%e&6ie " #l "nel'% BPD) şi ADS)/
