如图,已知在△ABC中,∠BAC=90°,AB=AC,点D在边BC上,以AD为边作正方形ADEF,联结CF,CE. (1)求证:FC⊥BC; (2)如果BD=AC,求证:CD=CE.
问题描述:
如图,已知在△ABC中,∠BAC=90°,AB=AC,点D在边BC上,以AD为边作正方形ADEF,联结CF,CE.
(1)求证:FC⊥BC;
(2)如果BD=AC,求证:CD=CE.
答
证明:(1)∵四边形ADEF是正方形,∴AD=AF,∠FAD=90°=∠BAC,∴∠FAD-∠DAC=∠BAC-∠DAC,∴∠FAC=∠BAD,在△ABD和△ACF中AB=AC∠BAD=∠FACAD=AF,∴△ABD≌△ACF(SAS),∴∠B=∠FCA,∵∠BAC=90°,∴∠B+...