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Consider the square ABCD whose diagonals, AC and BD, meet at X.AB is parallel to DC and AC intercepts them. Therefore <BAX = <DCX.
AB is parallel to DC and BD intercepts them. Therefore <ABX = <CDX.
AB = CD.
Therefore triangle ABX is congruent to triangle CDX (SAS).
So AX = XC ie X is the midpoint of AC and BX = XB ie X is the midpoint of BD.
ie the diagonals bisect each other.
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