\"\"Explore:   Plot the vertices on a coordinate plane.

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Plan:

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If the diagonals are perpendicular, then ABCD is either a rhombus or a square.

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The diagonals of a rectangle are congruent. If the diagonals are congruent and perpendicular, then ABCD is a square.

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\"Graph\"\" Solve:

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Use the Distance Formula to compare the lengths of the diagonals.

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The distance formula is  \"\".

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\"\"   (Substitute \"\")

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\"\"                         (Simplify)

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\"\"     (Substitute \"\")

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\"\"                        (Simplify)\"\"

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Use slope to determine whether the diagonals are perpendicular.

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The slope formula is \"\".

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Slope of   \"\"        (Substitute \"\")

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                 \"\"

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Slope of  \"\"            (Substitute \"\")

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                 \"\"\"\"

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Since the slope of \"\" is the negative reciprocal of the slope of \"\", the diagonals are perpendicular. \"\" and \"\"  have the same measure, so the diagonals are congruent. ABCD is a rhombus, a rectangle, and a square. \"\"ABCD is a rhombus, a rectangle, and a square.