如图所示,AD⊥AB,AE⊥AC,且AD=AB,AE=AC.试说明:BE=CD,BE⊥CD
问题描述：
如图所示,AD⊥AB,AE⊥AC,且AD=AB,AE=AC.试说明:BE=CD,BE⊥CD
答
∠DAB=∠DAE+∠EAB=90°
∠CAE=∠DAE+∠CAD=90°
∴∠EAB=∠CAD
且AD=AB,AE=AC
∴△CAD=△EAB
∴BE=CD
延长BE交CD于F
∵△CDA=△EAB
∴∠CDA=∠EBA=∠FBA
∠CDB+∠DBF=∠CDA+∠ADB+∠DBF=∠FBA+∠DBF+∠ADB=∠DBA+∠ADB=90°
∴∠DFB=90°
∴BE⊥CD