摘要： 数学课上.李老师出示了这样一道题目:如图.正方形的边长为.为边延长线上的一点.为的中点.的垂直平分线交边于.交边的延长线于.当时.与的比值是多少? 经过思考.小明展示了一种正确的解题思路:过作直线平行于交.分别于..如图.则可得:.因为.所以.可求出和的值.进而可求得与的比值. (1) 请按照小明的思路写出求解过程. (2) 小东又对此题作了进一步探究.得出了的结论.你认为小东的这个结论正确吗?如果正确.请给予证明,如果不正确.请说明理由. (1)解:过作直线平行于交.分别于点.. 则... ∵.∴.····························································································· 2分 ∴.. ∴. ···································································································· 4分 (2)证明:作∥交于点.················································································ 5分 则.. ∵. ∴. ∵.. ∴.∴.······························································ 7分 ∴.····················································································································· 8分

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