Is a square a rectangle?

The Rectangle

A rectangle is a parallelogram whose sides intersect at 90° angles.  Now, since a rectangle is a parallelogram, its opposite sides must be congruent.

The Square

A square is also a parallelogram whose sides intersect at 90° angles. Therefore, like a rectangle its opposite sides are congruent. However, a square has an added feature. It is also a rhombus. Therefore, all of its sides are congruent.

A rectangle is a square when both pairs of opposite sides  are the same length. This means that a square is a specialized case of the rectangle and is indeed a rectangle. 

What extra properties does the square have? 

Well, the only difference is that a square is also a rhombus so the square has all the properties of a rhombs while a rectangle does not.