Question

如图,△ABC中,∠BAC=90°,AD⊥BC,垂足为D,∠ABC的平分线交AD于E,交AC于F,△AEF是等腰三角形吗

Answer 1

△AEF是等腰三角形．

∵BF平分∠ABC,

∴∠ABF=∠DBF,

又∵∠BAC=90°,AD⊥BC,

∴∠AFE=90°-∠ABF,∠DEB=90°-∠DBF,

∴∠AEF=∠DEB,

又∵∠DEB=∠AEF,

∴∠AEF=∠AFE,

∴△AEF是等腰三角形．