如图.AB=AC,AB的垂直平分线交AC于D点,若AD=BC, (1)求∠B; (2)若点E在BC的延长线上,且CE=CD,连AE,求∠CAE.

问题描述:

如图.AB=AC,AB的垂直平分线交AC于D点,若AD=BC,

(1)求∠B; 
(2)若点E在BC的延长线上,且CE=CD,连AE,求∠CAE.

(1)连接BD,设∠BAC=x°,∵AB的垂直平分线交AC于D点,∴AD=BD,∴∠ABD=∠BAC=x°,∴∠BDC=∠BAC+∠ABD=2x°,∵AD=BC,∴BD=BC,AB=AC,∴∠BCD=∠ABC=2x°,∴5x=180,解得:x=36,∴∠BAC=36゜,∠ABC=72゜;...