1 It is a two dimensional shape that has four sides
2 It belongs to the class of polygons known as quadrilaterals
3 It can be called an oblong
4 It can be a golden rectangle which has special properties
5 It has a perimeter which is the sum of its sides
6 It has an area which is its length times its width
7 It has four interior right angles
8 It has exterior angles that add up to 360 degrees
9 It has two equal diagonals
10 It has two lines of symmetry
11 It has two pairs of parallel sides
12 It can be used in conjunction with Pythagoras' theorem
13 It can be circumscribed by a circle
14 It can be plotted on the Cartesian plane
15 It is possible to find its dimensions given only its perimeter and area
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The essential properties are that a rectangle is a quadrilateral whose sides met at right angles. There are many other properties but all of them follow from this.
Yes. There is a shape that has all the properties of a rectangle and all the properties of a rhombus at the same time. It is called a square.
A rectangle is a parallelogram with angles of 90 degrees. A square has those properties (and more) so it is a rectangle.
For a start, a square IS a rectangle, so it has ALL the properties of a rectangle. A square has the additional property that all of its sides have the same length.