Problem #PRU-98426

Problems Geometry Plane geometry Quadrilateral Parallelogram Special cases Rectangles and squares. Criteria and properties

Problem

A square is cut by 18 straight lines, 9 of which are parallel to one side of the square and the other 9 parallel to the other – perpendicular to the first 9 – dividing the square into 100 rectangles. It turns out that exactly 9 of these rectangles are squares. Prove that among these 9 squares there will be two that are identical.