What words do not rhyme with cat?

Oh, the question is not nearly that easy to ask or to answer. There are probably more than 4 Words that lack a perfect rhyme, but almost any Word, even the ones you are thinking of, could be worked into a rhyme scheme somehow. One question would be: Why even be concerned about rhyme? Apart from being a fun pastime, rhyming is no longer considered a central element of verse, and it usually gets in the way. Writers today don't have a fraction of the skill that poets of a different time had when it comes to the art of rhyme.

I heard this creative rhyme for 'orange' on an NPR radio broadcast several years ago, and I do not recall the writer, who certainly deserves to be given credit for it. I couldn't even find it searching the local NPR/PBS station programming histories. This is one of the most playful, original and delightful rhymes I've ever heard.

Four engineers

Wore orange brassieres.