Question

如图,在△ABC中,BD⊥AC,CE⊥AB于点D,E点,尝试探索∠ADE与∠ABC的大小的关系,

Answer 1

证明：延长BA,CE,两线相交于点F∵BE⊥CE∴∠BEF =∠BEC = 90?BR>在△BEF和△BEC∠FBE =∠CBE,BE = BE,∠BEF =∠BEC∴△BEF≌△BEC（ASA）∴EF = EC∴CF = 2CE∵∠ABD +∠ADB = 90?稀所以CF +∠CDE = 90?BR>此外∵∠ADB =∠CDE∴∠ABD =∠ACF在△ABD和△ACF∠ABD =∠ACF,AB = AC,∠BAD =∠CAF = 90?BR>∴△ABD≌△ACF（ASA）∴BD = CF∴BD