One of the basic solutions is given in the
illustration. When you move the entire bottom triangle of three
matches to the new position as shown, the three initial triangles
remain plus one additional, smaller, equilateral triangle appears.
Another creative solution (though it employs 5 triangles instead of
required 4) to this puzzle was sent to us by Joćo Gratuliano (see the
bottom illustration). Describing this "Christmas Tree 3D creative
solution" the author of it writes:
Another great solution is to get 5 triangles, putting 3 matches over
one triangle, making a pyramid of base 3...
Thank you, Joćo for this creative solution.