Some details missing in your question, but I will try to answer in general.  
A TRIAC operates in an AC circuit, provided that the particular conditions of a thyristor are met, that is, not exceed the **maximum working voltage** and ensure minimal **[holding-current][1]**.

You must not forget that **to synchronize the switching of the TRIAC**, you must take into account the zero crossing of the winding that feeds the circuit of the TRIAC.

If you can ensure this operations conditions, the TRIAC will function in the secondary of an isolation transformer.

Edit: zero-crossing & pulse
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Synchronization with the zero crossings of the line, allows you to control the power applied to the load.
Basically it is turning on the TRIAC after a certain time after the line voltage zero crossing.
There are many methods to detect the zero crossing and to generate the shot. It would be very extensive to list them all here.

[Here][2] you can access information about [phase control][3] using a TRIAC.
[Here][4] you will find information to turn a TRIAC completely in sync, without power control.


  [1]: http://electronics.stackexchange.com/questions/48725/what-is-the-holding-current-on-a-triac
  [2]: http://www.littelfuse.com/~/media/electronics/application_notes/switching_thyristors/littelfuse_thyristor_phase_control_using_thyristors_application_note.pdf.pdf
  [3]: https://en.wikipedia.org/wiki/Phase-fired_controllers
  [4]: https://www.fairchildsemi.com/application-notes/AN/AN-3004.pdf