Question

三角形abc中,ab等于ac,d在ac上,e在ac延长线上,且bd等于ce,de交bc于p,求证dp等于ep

Answer 1

证明：过D作DF∥AC交BC于F,

则∠DFB=∠ACB,∠PDF=∠PCE,∠PFD=∠E,

∵AB=AC,∴∠B=∠ACB,

∴∠DFB=∠B,∴BD=DF=CE,

∴ΔPDF≌ΔPEC,

∴PD=PE.