Question

（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．

Answer

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