If you draw a triangle strip with the same vertices as a quad, you should get the same output visually as you would have with the quad.
The only trick is that you need to reorder your vertices. Consider this shape...
UL---UR
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| |
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LL---LR
Perhaps you've ordered your vertices LL, LR, UR, UL. This produces a counter-clockwise winding of the face producing the whole of the shape. However, it won't work for a triangle strip, because strips require that the last two vertices of the previous triangle make up one of the edges of the next triangle. That means that the second and third vertices here need to be a diagonal, but instead here they are an edge (LR, UR is the right edge of the quad).
If you reorder your vertices like this LR, UR, LL, UL then you get the following result when treated as a triangle strip..
UL---UR
| /|
| / |
|/ |
LL---LR
OpenGL will then interpret this as two triangles with the vertices LR, UR, LL and LL, UR, UL.
A given quad strip can similarly be converted into a triangle strip by reordering the vertices.