Yes, infact there is 5 ways.
1. with two pieces.
2. with three pieces.
3. with four pieces
4. with five pieces
& 5. with seven pieces.
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Sort of depends on how the two triangles are beforehand. One nice way to make four equilateral triangles from six matchsticks is to make a tetrahedron (a triangular pyramid).
Here is one way: /\ --- /\/\ ----- These are {45°, 45°, 90°} triangles. There are 3 on the bottom row, and 1 on top. Actually, any four identical isosceles triangles would work.
If the triangles are congruent and you match the hypotenera the right way, you can get a rectangle. If the triangles are not congruent, you can't even necessarily get a quadrilateral.
There is more than one way to join two triangles. It would be possile to assemble a parallelogram out of two congruent equilateral triangles.
NO, equilateral ONLY refers to TRIANGLES