[tex]\it a) \ ABCD-dreptunghi\\ \\ AD=BC=12cm \Rightarrow AR=RD=12:2=6cm\\ \\ CD=AB=18cm \Rightarrow DQ=QP=PC=18:3=6cm\\ \\ \Delta RQD-dreptunghic,\ \widehat D=90^o,\ \ RD=DQ=6cm \Rightarrow \\ \\ \Rightarrow \Delta RQD-\ dreptunghic\ \ isoscel[/tex]
[tex]\it b)\ ABCD-dreptunghi \Rightarrow CD||AB,\ \ P,\ Q\in CD \Rightarrow PQ||AB \Rightarrow AQPB-trapez\\ \\ \Delta DAQ\equiv \Delta CBP\ (catet\breve a-catet\breve a) \Rightarrow AQ=BP \Rightarrow AQPB-trapez\ isoscel[/tex]
[tex]\it c)\ Fie\ AP\cap BQ=\{O\}\\ \\ \Delta ADP-dr.is.\ (AD=DP=12cm) \Rightarrow \widehat{APD}=45^o\\ \\ \Delta BCQ-dr.is.\ (BC=CQ=12cm) \Rightarrow \widehat{CQB}=45^o\\ \\ Din\ \ \Delta OPQ \Rightarrow \widehat{QOP}=180^O-45^o-45^o=90^o \Rightarrow BQ\perp AP[/tex]
