Each of the sides BC,CA,AB of the triangle ABC was divided into three equal parts and on the middle sections of these sides as bases, equilateral triangles were built outside the triangle ABC, the third vertices of which were marked with the letters A′,B′,C′ respectively. In addition, points A′′,B′′,C′′ were determined, symmetrical to A′,B′,C′ respectively with respect to the lines BC,CA,AB. Prove that the triangles A′B′C′ and A′′B′′C′′ are equilateral and have the same center of gravity as the triangle ABC. geometryEquilateralequilaterals