梯形ABCD,AD//BC,AB=AC,BC=BD,AB垂直AC,对角线AC,BD交与点O求证；OC=DC
问题描述：
梯形ABCD,AD//BC,AB=AC,BC=BD,AB垂直AC,对角线AC,BD交与点O求证；OC=DC
答
证明：过点A作AE⊥BC,交BC于点E；过点D作DF⊥BC,交BC于点F.易证AE=DF又因为AB=AC,AB⊥AC所以∠ABC=∠ACB=45°还有∠BAE=∠CAE=45°从而AE=BE=CE=BC/2又因为BC=BD所以DF=AE=BC/2=BD/2从而∠DBF=30°又易知∠BCD=∠BDC...