### Transformation of triangle in rectangle

In the triangle we have the straight line HE passing through the midpoints of sides AB and AC, and the segment
GA perpendicular to this straight line. As the colors indicate, using
trapezoid BCEH and triangles AHG and EAG we can construct the rectangle with the
same area as the triangle. Intuitively we can see that the parts that make up the triangle also make the rectangle.

If our purpose is to remain inside of the spirit of deductive geometry,
we must show that the triangular regions that complete the rectangle obtained
from the trapezoid are in fact congruent to the smaller triangles that are
part of the original given triangle. To see the demonstration here click

Transform rectangle to square

It comes back to the Presentation