Let A, B, C, D be vertices of a parallelogram with AB : D, B =...

 

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Let A, B, C, D be vertices of a parallelogram with AB : DỜ, BỜ = AD. If the distance = between A and C is equal to the distance between B and D, we claim that the parallelogram must be a rectangle. Let's show this with vectors. (a) Which pair from the following vectors must be of equal magnitude? Write the corresponding equation with the magnitude of those vectors on each side. AB, AĎ, AB + AĎ, AB – AĎ, AB + CD (b) Rewrite the equation from Part (a), using an appropriate property relating magnitude to the dot product. (c) Simplify the equation from part (b) to obtain a justification that the vertices A, B, C, D form a rectangle. Let A, B, C, D be vertices of a parallelogram with AB : DỜ, BỜ = AD. If the distance = between A and C is equal to the distance between B and D, we claim that the parallelogram must be a rectangle. Let's show this with vectors. (a) Which pair from the following vectors must be of equal magnitude? Write the corresponding equation with the magnitude of those vectors on each side. AB, AĎ, AB + AĎ, AB – AĎ, AB + CD (b) Rewrite the equation from Part (a), using an appropriate property relating magnitude to the dot product. (c) Simplify the equation from part (b) to obtain a justification that the vertices A, B, C, D form a rectangle.