Quadrilateral properties should be established, not simply recited. A diagonal often divides a quadrilateral into triangles; if those triangles can be shown congruent, corresponding side and angle properties follow.
For a parallelogram, a diagonal creates two triangles with a shared side. Parallel sides provide equal alternate angles, allowing congruence and therefore opposite sides/angles to be related. Similar reasoning supports properties of rectangles, rhombuses and squares.
Classification is hierarchical: a square satisfies the definitions of a rectangle and a rhombus as well as being a square. Always use stated properties—parallel sides, equal sides, angles, diagonals and symmetry—not how the sketch looks.
Preserve the practical AC9 context by applying quadrilateral geometry to mechanisms such as car jacks, scissor lifts, folding umbrellas, toolboxes and cherry pickers, where changing angles and rigid bars control movement.