如图，AD为△ABC的角平分线，DE⊥AB于点E，DF⊥AC于点F，连接EF交AD于点G．

（1）求证：AD垂直平分EF；

（2）若∠BAC=60°，猜测DG与AG间有何数量关系？请说明理由．

小明发现这三种方案都能验证公式：

a²+2ab+b²=（a+b）²，

对于方案一，小明是这样验证的：

a²+ab+ab+b²=a²+2ab+b²=（a+b）²

请你根据方案二，方案三，写出公式的验证过程。

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