What is the difference between a quadrilateral, trapezoid, parallelogram, rectangle and square?

Here we cover the different types of quadrilaterals: trapezoids, parallelograms, rectangles and squares!
Please note that this list is not exhaustive. For example, the rhombus (diamond shape) is not covered here as it is really a special type of parallelogram. (The rhombus is a parallelogram where all 4 sides are equals.)