过c做CE⊥AB于E
△AEC≌△ADB
CE=DB
PM//CE
BP/BC=PM/CE①
PN//BD
CP/BC=PN/BD②
①②左右同时加在一起
BP/BC+CP/BC=PM/CE+PN/BD=PM/BD+PN/BD=(PM+PN)/BD
=(BP+CP)/BC=1
所以PM+PN=BD
(2)过C做CF⊥MP于F
∠FPB=90-∠B=90-∠ACB=90-∠PCN=∠CPN
△PFC≌△PNC
PN=PF
MF=CE
MP=MF+FP=CE+PN
结论MP=CE+PN
过c做CE⊥AB于E
△AEC≌△ADB
CE=DB
PM//CE
BP/BC=PM/CE①
PN//BD
CP/BC=PN/BD②
①②左右同时加在一起
BP/BC+CP/BC=PM/CE+PN/BD=PM/BD+PN/BD=(PM+PN)/BD
=(BP+CP)/BC=1
所以PM+PN=BD
(2)过C做CF⊥MP于F
∠FPB=90-∠B=90-∠ACB=90-∠PCN=∠CPN
△PFC≌△PNC
PN=PF
MF=CE
MP=MF+FP=CE+PN
结论MP=CE+PN