yes. They are. because it is both equilateral and equiangular, the diagonals are at the same angles to the sides (45 degrees) and that angle makes them perpendicular.
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The diagonals of a rectangle are never perpendicular but the diagonals of a square are perpendicular
Yes, the diagonals of a rhombus are perpendicular.
The diagonals of a rhombus are perpendicular
Yes the perpendicular diagonals intersect at right angles or 90 degrees
Sure, a square is a rectangle and the diagonals of a square are perpendicular.