Question

已知如图,在△BFC中,BE,CA分别是边FC,BF上的高,BE与CA相交于D,PE平分∠ABC,AB=AC,求证:∠F

Answer 1

∵在△ABC中,AB=AC,∠BAC=90°∴∠ABC=∠ACB=45°BE平分∠ABC,所以∠ABE=∠EBC=22.5°在△FBE中,∠F=180°-∠ABE-∠BEF=67.5°在△FBC中,∠BCF=180°-∠F-∠FBC=67.5°所以∠F=∠BCF