Question 566546: Quadrilateral abcd has vertices a(-5,6) b(6,6)c(8,3) and d(-3-3).
Prove quadrilateral abcd is a parallelogram but is neither a rhombus nor a rectangle.
Answer by solver91311(24713)   (Show Source):
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Using the vertex data given and the slope formula, calculate the slopes of the four lines that contain the side segments.
where ) and ) are the coordinates of the given points.
If it is a parallelogram, then the results of the first step will be that two of the lines have slopes equal to each other and the other two slopes are also equal to each other.
If the two non-equal slope numbers are not negative reciprocals, then the non-parallel sides are not perpendicular. (in this case, one of the slopes is zero, so if the lines were perpendicular, the other slope would be undefined) If the non-parallel sides are not perpendicular, then the figure cannot be a rectangle.
Use the distance formula
^2\ +\ (y_1\ -\ y_2)^2})
to calculate the measure of one of the sides. Then do it again for one of the sides not parallel to the first one. If the measures are different, the figure cannot be a rhombus.
By the way, label vertices with upper case and sides with lower case.
John
My calculator said it, I believe it, that settles it
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