Show that the marked triangle is an equilateral triangle




The angle at \(A\) equals \(60^\circ\) because it is one of the angles of the big equilateral triangle.
The sides \(AB\) and \(AC\) have the same length because they are symmetric with respect to the height of the big equilateral triangle passing through \(A\).
The triangle ABC is isosceles and with one angle equal to \(60^\circ\) hence it is an equilateral triangle.