Completion requirements
Read this chapter, which summarizes all properties of various quadrilaterals, including the properties of their diagonals.
Hierarchy of quadrilaterals
Notice that properties of quadrilaterals overlap. A square is not only a square, but also a rhombus, a rectangle, a parallelogram, and a quadrilateral. This means that a square will have all the same properties as rhombuses, rectangles, parallelograms, and quadrilaterals.
The following diagram shows the hierarchy of quadrilaterals.