Write a Prolog program that stores information about geometric objects. You must construct the geometric objects basing on simpler forms. The objects to construct are:

2D Point

Segement, can be represented with two 2D points or one 2D point, a slope, and a length

Square

Rectangle

Circle

The program must be able to answer the following questions:

English	Prolog
Is this segment parallel to this other line?	parallel( segment(point2d(x,y), point2d(x,y)), segment (point2d(x,y), point2d(x,y)))
Is this segment perpendicular to this other line?	perpendicular( segment (point2d(x,y), point2d(x,y)), segment (point2d(x,y), point2d(x,y)))
Is this segment contained in this polygon?	contained( segment(point2d(x,y), point2d(x,y)), circle(point2d(x,y),r))
Is this polygon contained in this other polygon?	contained( square(point2d(x,y), length), circle(point2d(x,y),r))
Does this polygon intersects this other polygon?	intersects( square(point2d(x,y), length), circle(point2d(x,y),r))
Is this segment vertical?	vertical(segment (point2d(x,y), point2d(x,y)))
Is this segment perpendicular?	perpendicular(segment(point2d(x,y), point2d(x,y)))
Is this point on the figure?	on(point2d(x,y), segment(point2d(x,y), point2d(x,y)))
Is this point in the figure?	in(point2d(x,y), circle(point2d(x,y),r))