I was trying to study some geometry, but I just can't seem to wrap my head around all this mathematical mumbo jumbo. Can you help me out?
Many an object of this type are familiar to geometers! (8)
A famous mathematician returned to sign with hat (6)
Legs itch, tea spilled (7)
A ring is nearly invalid inside a bum (7)
A parallelogram partially gets started backtracking on a weekday (6)
Concise line made more concise line on regular polygon (7)
The above postulates are supposed to help me solve the below equation, which I think my professor called the Vigenere Theorem or something... I don't quite remember because it was early and I was very sleepy.
Y vxseztmxzfcgu lu c nxbppn seu nlutxre qjfwtz emvn kwjrbmvx
TRIANGLE? (This looks like a cryptic definition, but "familiar" or "family" don't seem to have any special meaning in geometry.)
EUCLID (reversal of CUE, plus LID)
CATHETI (anagram of "itch tea", definition "legs")
ANNULUS (NUL(-l) inside ANUS)
GNOMON (start of "Gets"; reversal of ON; MONday)
??? (Answer likely hexagon / octagon / nonagon / decagon / megagon - the last seems plausible given that "line" could be GAG (as in a joke). If "Concise line made more concise" could give ME, that would complete the wordplay.)
decrypting the given string with all the answers concatenated. This didn't seem to give anything useful. I've also tried decrypting with the guesses I have so far, and then breaking the remaining Vigenere cipher with usual cryptographic techniques. This also didn't work, so either that's not correct either, or both TRIANGLE and MEGAGON are wrong.