Question

（本小题满分7分）如图，四边形中，，
平分，交于．

【小题1】（1）求证：四边形是菱形；
【小题2】（2）若点是的中点，试判断的形状，并说明理由．

Answer 1

【小题1】（1），即，又，四边形是平行四边形．
····································································································· （2分）
平分，，················································ （3分）
又，，，，
四边形是菱形．
【小题2】（2）证法一：是中点，．
又，，，······································· （5分）
，··························································· （6分）
，．
即，是直角三角形．··············································· （7分）
证法二：连，则，且平分，·········································· （5分）
设交于．
是的中点，．························································· （6分）
，是直角三角形．解析:
略