Question

如图,△ABC中,BC上一点D到AB、AC的的距离相等,P是AD上一点,PE∥AB交BC与E,

Answer 1

设DM⊥AB于M,DN⊥AC于N

∴DM=DN

∵AD=AD

∴RT△ADM≌RT△ADN(HL)

∴∠DAB=∠DAC

∵PE∥AB,PF∥AC

∴∠DPE=∠DAB,∠DPF=∠DAC

∴∠DPE=∠DPF

即PD平分∠EPF