题目

题型：不详难度：来源：

(12分) 如图，在△ABC中，ME和NF分别垂直平分AB和AC．

(1)   若BC =" 10" cm，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