A truss bridge gains it's strength from the numerous triangular forms contained in it's structure. Were the structural members of the span arranged in rectangles instead of triangles, the bridge would be weak and collapse. This is because in a rectangle, a lateral force can change the angles without changing the lengths of any of the sides (the beams), allowing the rectangle to collapse without any compressive or tension forces to resist the collapse.
But in a triangular object (or I think any other polygon with an odd number of sides - isn't that right?) you cannot change the angles without changing the lengths of the sides. So the beams push back on any force that tries to change their shape. Since the triangle has the least number of angles of any odd sided figure, even a small change in angle would require a large change in side length, resulting in a large resistive force.