Question

subiectul 3 va rog ( 99 de puncte )

Answer 1

$7)~[AO] \equiv [CO]~si~ m( \angle AOC)= 90 \textdegree \Rightarrow \Delta AOC-dreptunghic~isoscel \\ \\ \Rightarrow m( \angle ACO)= 45 \textdegree .~~~~~~~~(1)$

$[BO] \equiv [DO] ~si~m( \angle BOD)=90 \textdegree \Rightarrow \Delta BOD -dreptunghic~isoscel \Rightarrow \\ \\ \Rightarrow m( \angle ODB)=45 \textdegree.~~~~~~~~(2) \\ \\ Din~(1)~si~(2)~rezulta~ca~AC~||BD~(alterne~interne).$

$8)~\Delta AOC-isoscel~\Rightarrow OM \perp AC,~insa~AC~||~BD,~de~unde~ \\ \\ rezulta~ca~OM \perp BD,~adica~ON \perp BD.~(pentru~ca~M,O,N~sunt \\ \\ coliniare). \\ \\ 9) ~\Delta BOD-isoscel~\Rightarrow ON \perp BD,~insa~BD~||~AC,~de~unde~ \\ \\ rezulta~ca~ON \perp AC,~adica~OM \perp AC.~(pentru~ca~M,O,N~sunt \\ \\ coliniare). \\ \\ OM \perp AC \Rightarrow M-mijlocul~lui~[AC]~(deoarece~\Delta~AOC~este~isoscel).$

DESEN: