It's not the syllable count that matters, it's that anytime you have words with common endings, or words with unnecessarily added endings (like we're doing here), the root words need to rhyme as well as the endings.
Example: -er words. You can rhyme "teacher" with "reacher", but not with "plumber", even though all three have the same endings, technically.
It has to do with which syllable is stressed. The last stressed syllable in the word (or in the line of poetry), and everything after it, has to be the same. So the "-eacher" in "teacher" and "reacher" are identical, and it's a good rhyme. To rhyme with "hex", the word has to end in "-ex." You can fudge the consonants after the stressed vowel just a bit, and get something that's not quite a rhyme, but good enough for, say, a HN comment. But you can't fudge the stressed vowel at all.