Ok, I'm going to be taking calc III next week, so I wanted to get a head-start by doing the MIT multivariable calculus opencourseware. While most of the material was easy, these proofs are really killing me. Here are two examples: Ex.1: Using vectors and dot product show the diagonals of a parallelogram have equal lengths if and only if it’s a rectangle. Ex. 2: The median of a triangle is a vector from a vertex to the midpoint of the opposite side. Show the sum of the medians of the triangle. Now, what I am wondering is if there's a specific type of method you utilize to prove these types of things? I feel like every time I try one on my own, I end up hitting a brick wall. I will figure out a handful of different restrictions and such, but I never seem to be able to tie up the loose ends. I don't need the answers to either example as they have them online. I am just lost as to a method to figure these types of problems out. If anyone has any strategies, I'm all ears.