如图,在△ABC中,AB=AC,∠BAC=40°,分别以AB,AC为边作两个等腰直角三角形ABD和ACE,使∠BAD=∠CAE=90°. (1)求∠DBC的度数; (2)求证:BD=CE.
问题描述:
如图,在△ABC中,AB=AC,∠BAC=40°,分别以AB,AC为边作两个等腰直角三角形ABD和ACE,使∠BAD=∠CAE=90°.
(1)求∠DBC的度数;
(2)求证:BD=CE.
答
(1)∵△ABD为等腰直角三角形,∴∠DBA=45°.又∵AB=AC,∠BAC=40°,∴∠ABC=70°.∴∠DBC=115°;(2)证明:∵△ABD和△ACE均为等腰直角三角形,∴∠BAD=∠CAE=90°,AB=AD,AC=AE.又∵AB=AC,∴AB=AD=AC=AE...