Yes, they do.
no
They are either kites or (if the diagonals bisect each other) rhombuses.
The diagonals of a rectangle do not cross at right angles
The diagonals of a square and a rhombus cross at right angles.
They are a square, a rhombus and a kite.
rectangle
No.
No
No.
No but they cross at right angles in a square
kite
yes, they do. though they are not always equal in length they always cross at right angles.
The diagonals of a kite cross each other at right angles