Does the Nyquist Sampling Theorem hold for a triangular wave?
The Nyquist sampling theorem holds for bandlimited signals.  Note that a perfect triangle wave is composed of a (convergent) infinite series of harmonics, which requires infinite bandwidth and is thus not bandlimited.

However, the energy remainder after a suffinciently large number of harmonics might be small enough than for a given noise floor that you can treat the portion of the triangle wave that is above that noise floor as bandlimited below some point above that last kept harmonic.