Rigorous rhymes with:
vigorous, vigorous, adulterous, adventurous, amorous, avarice, barbarous, boisterous, cancerous, cantankerous, carboniferous, carnivorous, coniferous, dangerous, decorous, fossiliferous, generous, glamorous, hatteras, herbivorous, heterosporous, homosporous, humerous, humerus, humorous, insectivorous, lazarus, lecherous, murderous, numerous, obstreperous, odorous, omnivorous, onerous, overgenerous, oviparous, ovoviviparous, phosphorous, phosphorus, ponderous, precancerous, preposterous, prosperous, rancorous, rapturous, rhinoceros, slanderous, sonorous, temerous, tetramerous, thunderous, timorous, traitorous, treacherous, unglamorous, uterus, vigorous, viviparous, vociferous
Rigorous sounds like:
racehorse, racehorses, racers, rackers, raisers, rakers, raucher's, razor's, razors, reassures, recharge, recourse, recross, regress, requires, rescuers, reseachers, research, research's, researches, resource, resources, resources', richcreek, rickers, riechers, rigors, riker's, rikers, rockers, rockrose, roger's, rogers, rogers', rogers's, rosaria's, rosaries