In isosceles trapezoid ABCD, AD / / BC, Mn are the midpoint of ADBC, EF are the midpoint of BM, cm As shown in the figure, in isosceles ladder ABCD, AD / / BC, m and N are the midpoint of AD and BC respectively, e and F are the midpoint of BM and cm respectively (1) If the quadrilateral menf is a square, please explore the quantitative relationship between the height of the isosceles trapezoid ABCD and the base BC, and prove your conclusion

(1) M and N are the midpoint of AD and BC respectively, so Mn is perpendicular to AD and BC, and E and F are the midpoint of BM and cm respectively, so en = FN = BM / 2, so menf is a diamond. (2) if a quadrilateral menf is a square, then as long as me is perpendicular to en, that is, BM is perpendicular to en and en = BM / 2, then MBN is an isosceles right triangle

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