In the square ABCD, e is the midpoint of BC, f is the point on CD, and CF = 14CD, try to judge whether △ AEF is a right triangle? Try to explain the reason

In the square ABCD, e is the midpoint of BC, f is the point on CD, and CF = 14CD, try to judge whether △ AEF is a right triangle? Try to explain the reason

Let the side length of a square be 4a, ∵ e be the midpoint of BC, CF = 14CD, ∵ CF = a, DF = 3A, CE = be = 2A. According to the Pythagorean theorem, af2 = ad2 + df2 = 16a2 + 9A2 = 25a2, ef2 = CE2 + CF2 = 4a2 + A2 = 5A2, AE2 = AB2 + be2 = 16a2 + 4a2 = 20a2, ∵ af2 = ef2 + AE2, ∵ AEF are right triangles

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