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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1. 2.

milcah answered 1 year ago

Prove the following for Euclidean Geometry. Provide general dynamic illustrations in GeoGebra. You will have to...

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in hyperbolic/modern geometry. Let C be a circle and z any complex number. Prove that the...

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Identify the molecular geometry for each of the following triatomic molecules using the VSEPR model. Then,...

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10.33 predict the shape or geometry of the following mol-ecules , using theVSEPR model A). SiF4...

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The following kets name vectors in the Euclidean plane: |a>, |b>, |c>. Some inner products: <a|a>...

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Prove that the following statements are equivalent. A. The Euclidean parallel postulate holds. B. Given any...

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