题目内容
【题目】如图，在△ABC中，ME和NF分别垂直平分AB和AC．
(1)若BC =10cm，试求△AMN的周长．
(2)在△ABC中，AB = AC，∠BAC = 100°，求∠MAN的度数．
(3) 在 (2) 中，若无AB = AC的条件，你还能求出∠MAN的度数吗？若能，请求出；若不能，请说明理由．
【答案】（1）
cm
（2）
（3）能，证明略。
【解析】
解：(1) ∵ME垂直平分AB
∴MA=MB·············································································· 1分
∵NF垂直平分AC
∴NA=NC··············································································· 2分
∴cm······················· 4分
(2) ∵AB = AC，
∴
······································································· 4分
∵MA = MB
∴
··································································· 5分
∵NA = NC
∴
··································································· 6分
∴·········································· 8分
(3) 能．理由如下：·········································································· 9分
∵MA = MB
∴∠MAB =∠B
∵NA = NB
∴∠NAC =∠C
∴
·································· 12分
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