Question

已知在三角形ABC中,角B=角C,BD,CE分别是角ABC,角ACB的平分线,AM垂直于BD于M,AN垂直于CE于N,

Answer 1

证明△AMB≌△ANC即可.∵△ABC是等腰△,∠B=∠C,∴AB=AC,∴∠ABM=∠ACN=½∠B﹙∠C﹚,∠M=∠N=90°,∴△AMB≌△ANC﹙AAS﹚∴AM=AN,∴△AMN是等腰△.