what am i?

Rectangle.

A rectangle can also be called a quadrilateral, the two length sides are the same and the two height sides are the same. All the angles are 90°, and tiling patterns need to be something that tessellates, and rectangles tessellate.

a square does not as it has 4 lines of symmetry, a parallelogram does not have all angles the same size, so it would be a rectangle and quadrilateral as a quadrilateral is any shape with four sides which a rectangle has

Sorry i missed the part saying all angels had to be the same. And all squares are rectangles and a square actually has 4 lines of symmetry while a rectangle fits the requirment of 2

i meant it has 4 two diagonally and two from the sides, do not know why i put that i did not have 4 :/