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

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 opposite C = is expressed as c2 = a2 + b2 - 2 b a cos . 4. Prove the theorem: The bisector of an angle of a triangle divides the opposite side into two segments which are proportional to the sides that include the angle.

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milcah answered 1 year ago

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