ILL 1985 Problem 2

We are given a triangle $ABC$ and three rectangles $R_1,R_2,R_3$ with sides parallel to two fixed perpendicular directions and such that their union covers the sides $AB,BC$ , and $CA$ ; i.e., each point on the perimeter of $ABC$ is contained in or on at least one of the rectangles. Prove that all points inside the triangle are also covered by the union of $R_1,R_2,R_3.$