Prove that the diagonals of a rectangle split it into two pairs of equal isosceles triangles.

Given a rectangle ABСK. The diagonals AC and BK, intersect at one point O and divide the rectangle into two pairs of equal isosceles triangles. Consider the BOС triangle and the AOK triangle. The BC side of the BOC triangle is equal to the AK side of the AOK triangle. The sides of the OB and OС of the ВOС triangle are equal to the sides of the AO and OK of the AOK triangle.
Consider triangle AOB and triangle KOС. Side AB of triangle AOB is equal to side CК of triangle KOС. The sides AO and OB of the AOB triangle are equal to the sides OK and OС of the KOС triangle.