Q: Prove that each diagonal of a parallelogram bisects each other
How do I attempt this?
Can I find the midpoints of the diagonals, then if they're the same, get the distance between this midpoint and the vertices? If they're the same, have I proved it?
In addition to "congruent triangles" (basic geometry) and "vectors", I might use "coordinate geometry". We can always set up a coordinate system so that one vertex is at (0, 0), another at (a, 0), a third at (b, c) and then the fourth must be at (a+ b, c). Now, it is easy to find the midpoint of each diagonal- that is, if you can use coordinate geometry- and we don't know that.