Question

三角形ABC中,AB=AC,AD垂直BC,说明AH=2BD

Answer 1

证明：∵AD⊥BC,BE⊥AC

∴∠BCE+∠CBE=90°,∠BCE+∠DAC=90°

∴∠CBE=∠∠DAC

又∵AE=BE,∠BEC=∠AEB=90°

∴△AEH≌△BEC

∴AH=BC

∵AB=AC,AD⊥BC∴BC=2BD

∴AH=2BD