Asserts rhymes with:
reasserts, inserts, reasserts, alerts, averts, bertz, blurts, burts, cherts, curt's, curts, desserts, dirt's, diverts, ertz, exerts, flirts, gertz, geurts, gurtz, hirtz, hurts, inserts, kertz, kirts, kurtz, mertz, mirtz, reasserts, reverts, schertz, schmertz, shirts, shurtz, skirts, spurts, squirts, sturtz, subverts, vertz, virts, werts, wertz, wirtz, worts, wurtz
Asserts sounds like:
accord's, accords, ackroyd's, akridge, aseritis, aujourd'hui's