Question

如图,在三角形ABC中,∠BAC=90°,AB=AC,点D在BC上,且BD=BA,点E在BC的延长线上,且CE=CA,求

Answer 1

（1）当∠BAC=90°时

∵BA=BD

∴∠BAD=90°-1/2∠B

∴∠CAD=1/2∠B

∵CA=CE

∴∠CAE=1/2∠ACB

∴∠DAE=1/2（∠ABC+∠ACB）=45°

所以不变

（2）当AB=AC时,∠B=∠ACB

∵CA=CE

∴∠CAE=1/2∠ACB

∵BA=BD

∴∠BDA=90°-1/2∠B

∴∠CAD=∠BDA-∠ACD=90°-1/2∠B-∠B

∴∠DAE=90°-1/2∠B-∠B+1/2∠B=90°-∠B

∴∠DAE=1/2（180°-2∠B）=1/2∠BAC