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Prove the following problems using the complex plane model of Euclidean geometry, in the spirit of...

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Basic Math

Prove the following problems using the complex plane model ofEuclidean geometry, in the spirit of Erlangen Program: 1. Provethat the diagonals of a parallelogram bisect each other. 2. Provethat the sum of the squares of the diagonals of a parallelogram isequal to the sum of the squares of all the sides of theparallelogram. 3. Prove the Cosine Law for triangles: In a trianglewith the sides a, b, and c, the square of the side opposite C = isexpressed as c2 = a2 + b2 - 2 b a cos . 4. Prove the theorem: Thebisector of an angle of a triangle divides the opposite side intotwo segments which are proportional to the sides that include theangle.

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