In a convex quadrilateral, the diagonals are perpendicular. What other property must the diagonals have for this quadrangle to be a rhombus?
Let us write down three basic requirements for the diagonals of the ABCD rhombus:
1) Diagonals AC and BD are mutually perpendicular (given by condition).
2) The diagonals by the point of intersection of T.O are divided in half, that is, for the diagonal AC, AO = OC, and for the diagonal BD, BO = OD.
Failure to meet at least one of these conditions means that ABCD is not a diamond. Moreover, these three conditions are sufficient conditions for both diagonals.
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