题目

（本小题满分7分）如图，四边形中，，平分，交于．1.（1）求证：四边形是菱形；2.（2）若点是的中点，试判断的形状，并说明理由．  答案： 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．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 

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