Put the triangles in a line alternately pointing up and down.
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you can't
You cannot make four triangles our of a quadrilateral by ONE line through it. One line can give you at most two triangles. Two lines, each running from one vertex of the quadrilateral to the opposite vertex, will give 4 triangles.
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).
No.
Rhombus