题目内容
(本小题满分14分)
在如图所示的一张矩形纸片(
)中,将纸片折叠一次,使点
与
重合,再展开,折痕
交
边于
,交
边于
,分别连结
和
.
1.(1)求证:四边形是菱形;
2.(2)过作
交
于
,求证:
3.(3)若,
的面积为
,求
的周长;
1.(1)连结交
于
,························ 1分
当顶点与
重合时,折痕
垂直平分
,················· 1分
,
····················· 2分
在矩形
中,
,
,···························· 3分
.···························· 3分
································ 4分
四边形
是菱形.
2.(2)证明:过作
交
于
,
由作法,,··························· 5分
由(1)知:,又
,
,···························· 6分
,则
······················· 7分
四边形
是菱形,
,
.········· 8分
3.(3)四边形
是菱形,
.······························ 9分
设,
,
,
······························· 10分
①························ 11分
又,则
. ②················ 12分
由①、②得:························· 13分
,
(不合题意舍去)················ 14分
的周长为
·················· 14分
解析:略

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