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To add to the other replies, here's the English page for rhyming schemes, which calls this pattern "XAXA".

https://en.m.wikipedia.org/wiki/Rhyme_scheme

A more notable version of the same idea, which includes more unrhymed lines, is double dactyl (XXXA XXXA). Though this is more for poetry/limerick, and not for mnemonics.

No worries, you're correct, those lines don't rhyme.

It's pretty common for English poetry and songs to only rhyme every other line

they don't. in both cases, only every other line is rhyming. hot and not, ice and nice.