∠CDE+∠EAD=90度∠CDE+∠DCE=90度∠EAD=∠DCE△DCE∽△DAC=>DC^2=DA*DED是BC中点=>BD=CD所以BD^2=DA*DE=>BD:DE=DA:BD又因为∠BDE=∠ADB所以△ABD∽△BED
