ProblemShow that if the diagonals of a rectangle intersect at right angles then, the rectangle is a square. 
> a := vector([a1,a2]); b := s*vector([a2,a1]);
a := [ a1, a2 ] b := s [  a2, a1 ]
Here the vectors "a" and "b" denote the sides of a general
rectangle on the plane. The scalar "s" is the ratio of the
lengths of the two sides. Here is the picture,

> diag1 := a+b: diag2 := ab:
> solve( angle(diag1,diag2) = Pi/2, s);
1, 1
so yes! it is a square. 