Particular cases of first-kind quasi-parallelograms of the Lobachevsky plane

In this paper, we consider particular cases of quasi-parallelograms, which are obtained by transferring to the Lobachevsky plane various characteristic properties of rhombuses, rectangles, and squares of the Euclidean plane related with their diagonals. The existence of these quadrangles is proved by using the Cayley–Klein model in the circle of the Euclidean plane.