One corner of a rectangular piece of paper is folded as shown. Prove that the red line segments are concurrent.

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## Solution

Let the intersection of AD and CF be G, ΔGAF∽ΔGDC, AG:GD=AF:CD (1) ∵

BF∥CE, ΔFAB∽ΔCDE, AF:CD=AB:DE (2)

Let the intersection of AD and BE be H, ΔHAB∽ΔHDE, AB:DE=AH:HD (3)

Due to (1)-(3), AG:GD=AH:HD, G and H are at the same point, ∴ red lines concurrent