Question 578916
You might want to explain what "Parallelogram Consecutive Angles Conjecture" is, because, even though all of us have experience with geometry, including perhaps projective geometry and non-Euclidean geometry, some of us might not know the exact terminology you use (it may differ from book to book). I'm assuming it states that the consecutive angles of a parallelogram add up to 180 degrees. In that case, it's a theorem, not a conjecture.


The proof relies on the postulate that if two parallel lines are cut by a transversal, then the two (same-side) angles add up to 180 degrees. Use that in your proof. An important skill to have is how to write proofs (not necessarily two-column proofs) -- something you have to learn if you pursue a degree in mathematics, science, philosophy, etc.