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一、试题呈现(2014年随州)已知两条平行线l1,l2之间的距离为6,截线CD分别交l1,l2于C,D两点.一直角的顶点P在线段CD上运动(点P不与点C,D重合)直角的两边分别交l1,l2于A,B两点.1.操作发现如图1,过点P作直线l3∥l1,作PE⊥l1,点E是垂足,过点B作BF⊥l3,点F是垂足.此时,小明认为△PEA∽△PFB,你同意吗?为什么?
First, the questions presented (Suizhou, 2014) know that the distance between two parallel lines l1, l2 is 6, the cross-section CD intersects l1, l2 in C, D two points. The vertex P of the straight angle moves on the CD segment. (Point P does not coincide with points C, D) The two sides of the right angle are intersected by l1 and l2 at A and B respectively. 1. The operation is found as in Fig. 1. The point P is the straight line l3∥l1, and PE⊥l1 is the point E. It is foot-pedal, point B is BF⊥l3, point F is foot-pedal. At this time, Xiaoming thinks △PEA∽△PFB, do you agree? Why?