That circuit should produce reasonable symetric triggering, as I understand it thats the purpose of the bridge with the output shorted with resistors.
Double check your circuit for faults, are all the diodes in the bridge ok?, is the diac in the trigger circuit ok, if you have a 0-30v bench supply you can test a diac, put a 1k resistor in line with it accross the supply, it should turn on depending on the diac at about 25 to 30v.
I'm splitting hairs here but you say the trigger pulse isnt symetric, do you mean the pulse at the gate of the triac?, or do you mean the o/p waveform isnt symetric?
Its possible that your circuit is ok component wise but having false triggering problems, sounds like your able to 'scope the o/p, if thats the case replace the transformer load with a incandescent light bulb and see if the waveform changes, maybe theres some ringing or noise back from the tranny messing things up.
Please post in english, everyone here does - post been deleted disregard.