1. The problem statement, all variables and given/known data The question says to find a proof for Cauchy's Inequality and then the Triangle Inequality. This is an elementary linear algebra class I'm doing, so I can't use inner products or anything. 2. Relevant equations 3. The attempt at a solution I got the proofs using algebra, but I'm having trouble seeing them geometrically. I want to draw a picture for Cauchy's Inequality but can't quite visualize it.