The diagonals of a kite are perpendicular to one another. A kite is a quadrilateral shape with two pairs of adjacent touching congruent equal-length sides. That is the pairs cannot have a side in common.
Disjoint means that the two pairs are totally.
A square is a rhombus with all right angles. It has two pairs of equal-length adjacent next to each other sides. Two pairs of sides. A kite is a member of the quadrilateral family and while easy to understand visually is a little tricky to define in precise mathematical terms.