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Let the vertices of the quadrilateral be $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

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Plot the vertices in a coordinate plane and connect the quadrilateral.

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Graph :

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Each two vertices form a line segment.

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Find the slopes of three sides of the quadrilateral.

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$\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ are sides and $\"\"$ and $\"\"$ are diagonals of the quadrilateral.

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The formula for slope is $\"\"$ .

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Find the slopes of sides of quadrilateral.

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the diagonals slopes of quadrilateral.

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the slope of $\"\"$ .

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$\"\"$

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$\"\"$ .

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Find the length of the sides of quadrilateral.

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Using distance formula $\"\"$ .

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Length of $\"\"$

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$\"\"$ units.

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Length of $\"\"$

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$\"\"$ units.

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Length of $\"\"$

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$\"\"$ units.

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Length of $\"\"$

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$\"\"$ units.

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Observe that, the slopes of opposite sides of quadrilateral are equal.

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The slopes of adjacent side of quadrilateral negative reciprocal to each other.

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The slopes of the diagonals $\"\"$ of quadrilateral are also negative reciprocal to each other.

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Parallel lines slopes are equal.

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Perpendicular lines slopes are negative reciprocal to each other.

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The opposite sides of the quadrilateral are parallel and adjacent sides are perpendicular.

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Diagonals are perpendicular.

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And opposite sides have equal length.

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Therefore, $\"\"$ and $\"\"$ are the vertices of rectangle.

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$\"\"$ and $\"\"$ are the vertices of rectangle.