A kite
The sides are equal The angle between adjacent sides is 90 degrees There are two diagonals The diagonals are equal in length The diagonals make 90 degrees with each other The diagonals make 45 degrees with the sides
A rectangle has 2 pairs of parallel sides and its diagonals are of equal length but do not cross each other at 90 degrees
rhombus
A rectangle
A parallelogram
A rhombus has unequal diagonals which intersect at right-angles.
Square (also rhombus)
No but its diagonals bisect each other at 90 degrees
None but the diagonals intersect at 90 degrees
A parallelogram (or rectangle) which is not a rhombus (or square).
prove any two adjacent triangles as congruent
A rectangle would fit the given description