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Thinking about Geometry

Review question

Why is this quadrilateral a rhombus but not a square?
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Ref: R6641

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Question

Draw a diagram showing points \(A(-3,1)\), \(B(4,2)\), \(C(9,-3)\), \(D(2,-4)\).

For the figure \(ABCD\) state and prove a fact (or facts) sufficient to ensure that it is a parallelogram.
State and prove an additional fact sufficient to ensure that \(ABCD\) is a rhombus.
Prove that \(ABCD\) is not a square.