How to test a TRIAC with just a digital multimeter and no external circuit
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. Testing first and third quadrant operation of a triac.

If your multimeter has a high enough diode test voltage and current then the circuit of Figure 1 might work. SW1 and 2 can be replaced by a piece of wire or paperclip.

I've never tried this so I'd be interested to know if it works.