Two-triangle symmetries

These symmetrical triangles are of different color on each side.

Investigate which of these configurations are possible. 

How do you explain it?

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Explanation

Indeed, the last configuration (orange-blue) cannot be done.

Note: Do triangles have an axis of symmetry? Are they isosceles (with two equal sides)?

When rotating the triangles we are doing it according to an axis, if the triangle does not have symmetry the silhouette does not match.

Look now at the three pieces that make up the decomposed triangle. Are they symmetrical? 

The symmetry axes of the three pieces are the bisectives of the angles of the triangles. Investigate what is called the point where the 3 bisectives and their properties join.