题目

阅读理解 Many people may not find the idea of visiting Beijing's Forbidden City just to see its cultural relics(遗迹)very exciting. But what if you got to see deer there too? That certainly sounds like a better day out. Nine deer were introduced into the Forbidden City, also known as the Palace Museum, on Sept. 26 and would make it their home until February. The beautiful animals are part of an exhibition on deer-related relics, including furniture, clothes and artworks. In ancient China, deer patterns(图案)could be seen on lots of items since lu—deer—were considered to be a lucky我们把对称中心重合,四边分别平行的两个正方形之间的部分叫“方形环”,易知方形环四周的宽度相等.一条直线l与方形环的边线有四个交点M、M′、N′、N.小明在探究线段MM′与N′N 的数量关系时,从点M′、N′向对边作垂线段M′E、N′F,利用三角形全等、相似及锐角三角函数等相关知识解决了问题.请你参考小明的思路解答下列问题:(1)当直线l与方形环的对边相交时,如图1,直线l分别交AD、A′D′、B′C′、BC于M、M′、N′、N,小明发现MM′与N′N相等,请你帮他说明理由;(2)当直线l与方形环的邻边相交时,如图2,l分别交AD、A′D′、D′C′、DC于M、M′、N′、N,l与DC的夹角为α,你认为MM′与N′N还相等吗?若相等,说明理由;若不相等,求出MM′N′N的值(用含α的三角函数表示).
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