Prove the following problems using the complex plane model of
Euclidean geometry, in the spirit of Erlangen Program: 1. Prove
that the diagonals of a parallelogram bisect each other. 2. Prove
that the sum of the squares of the diagonals of a parallelogram is
equal to the sum of the squares of all the sides of the
parallelogram. 3. Prove the Cosine Law for triangles: In a triangle
with the sides a, b, and c, the square of the side...