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foldina a rectangle paper 3 times

Source: 2023 May Olympiad L2 p4

March 24, 2024
geometryrectanglepaperfolding

Problem Statement

Matías has a rectangular sheet of paper ABCDABCD, with AB<ADAB<AD.Initially, he folds the sheet along a straight line AEAE, where EE is a point on the side DCDC , so that vertex DD is located on side BCBC, as shown in the figure. Then folds the sheet again along a straight line AFAF, where FF is a point on side BCBC, so that vertex BB lies on the line AEAE; and finally folds the sheet along the line EFEF. Matías observed that the vertices BB and CC were located on the same point of segment AEAE after making the folds. Calculate the measure of the angle ∠DAE\angle DAE. https://cdn.artofproblemsolving.com/attachments/0/9/b9ab717e1806c6503a9310ee923f20109da31a.png
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