ABCD is a rhombus and P, Q, R, and S are the mid point of the side AB BC CD and DA respectively . show that the quadrilateral PQRS is a rectangle
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You first need to prove that PQRS is a parallelogram through the midpoint theorem (see your textbook for more info). Then, using the properties of parallel lines, show that two co-interior angles (that are supplementary) are equal. That'll give you 90-degree bisection angles. Using again the same property, you can show that each angle is 90 degrees AND ONLY the opposite sides are equal,
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