Four equal triangles problem

Challenge yourself with this triangle problem.

Squares were constructed on each side of triangle ABC. The free points of the squares were connected forming three more triangles. It is claimed that all the four triangles have equal area. Do they? Show that they do or don’t.

Hints:

1. Make a simpler problem. Use an isosceles triangle or right triangle for the triangle ABC.
2. Get ideas from the post Transforming a quadrilateral into a triangle with the same area.