yes, they do. though they are not always equal in length they always cross at right angles.
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The diagonals of a rhombus intersect (meet) at right angles.
The 2 diagonals of a rhombus intersect at right angles
A kite, a rhombus (special case of a kite), a square (a special case of rhombus).
Rhombus rhombus
A rhombus has no right angles at its vertices but its diagonals are perpendicular to each other forming 4 right angles.