Can you assume symmetry to compute the forces in the members

Can you assume symmetry to compute the forces in the members? Justify in one line. A is a pin joint and O is a roller.

4.8 ft 4.8 ft 4.8 ft 4.8 ft 500 lb 500 lb 1500 lb 500 lb 500 lb 500 lb 250 lb H 250 lb 250 lb N 9.6 ft G I CI E 6 ft 6 ft 6 ft 6 ft

Solution

since no horizontal forces act, the horizontal reaction reaction force at A becomes zero. thus at both A and O, there exits only vertical reaction forces.

But for this load configuration, symmetry cannot be assumed, since the forces on the left and right off the truss does are not equal.At B, 500 lb force acts, while at its equivalent symmetrical point N, 250 lb force acts.