To inscribe a square into a parallelogram, the necessary condition is that the parallelogram must have equal adjacent sides, making it a rhombus. This ensures that the angles are right angles, allowing for the square to fit perfectly within the shape. Participants are encouraged to share their thoughts and approaches to solving this geometric problem. The discussion emphasizes the importance of understanding the properties of parallelograms and squares in relation to each other. Ultimately, the geometric relationship between the two shapes dictates the possibility of inscribing a square.