题目内容
(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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