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The second problem is to prove the equilateral triangle in junior high school mathematics.
Solution: Because quadrilateral ABCD is a square.

So AD=CD

Because the crease at point D is that A falls on A'

So AD = AD

So A'D=CD.

And because e and f are the midpoint between ab and CD.

So EF is perpendicular to CD, that is, A'F is perpendicular to CD.

So triangle A'CD is an equilateral triangle.