如圖,點
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是等腰直角△

的直角邊

上一點,

的垂直平分線

分別交
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、
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、
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于點
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、
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、
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,且
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.當
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時,試說明四邊形

是菱形.

解:如圖,過點

作

⊥
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于點
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,
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∵
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,
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,
∴ △
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是等腰直角三角形,

∵
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,
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,∴
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.
又
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,
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,
∴ △

≌△
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,∴
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.
∵

是
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的垂直平分線,∴

,
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,
∴
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,
∴ △

≌△
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,∴

,
∴ 四邊形

是菱形.
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