题目

To travel around the world is the dream of many adventurous (爱冒险的) people. But very few people can afford a global tour because hotels, food and airplane tickets are too expensive. Some people, however, have thought of some ways to realize their dreams. Laura Cody and Tanbay Theune, a couple from Britain, decided to travel around the world. They have found a good way to pay for their trips. They look after pets for rich house owners. In exchange, they can stay in the houses for free. They have looked after horses, cows, cats, dogs and fish. In two years, the couple has been to （2007•湘潭）如图，在△ABC中，AB=AC，E，F分别为AB，AC上的点（E，F不与A重合），且EF∥BC．将△AEF沿着直线EF向下翻折，得到△A′EF，再展开．（1）请证明四边形AEA′F为菱形；（2）当等腰△ABC满足什么条件时，按上述方法操作，四边形AEA′F将变成正方形．（只写结果，不作证明）