Question

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．   

Answer

（1）cm

（2）

（3）能，证明略。

【解析】

【解析】
(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