A regular hexagon is given. Prove that if you successively connect the seridines of its sides by segments, you get a regular hexagon.

Let the side of the larger hexagon be A. Connect the serids of the sides of the hexagon. (It is recommended to build a drawing) Consider 6 triangles formed by the sides of a smaller hexagon and a larger one. They are isosceles (the bases are the sides of the smaller hexagon). On the basis of SUS (Lateral sides = A / 2, the angles between them are the corners of a regular hexagon), these triangles are congruent => bases, which are the sides of a smaller hexagon, are congruent => The smaller hexagon is regular.