SOLUTION: 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

Algebra ->  Parallelograms -> SOLUTION: 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       Log On


   

Question 855809: 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 KMST(5328) About Me  (Show Source):
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Points A and B have y=6 , so segment AB is part of the horizontal line y=6 .
According to their x-coordinates, B is to the right of A (because 6%3E-5 ).
The length of AB is 6-%28-5%29=6%2B5=11 .
Points C and D have y=-3 , so segment CD is part of the horizontal line y=-3 ,
with C to the right of D (because 8%3E-3 ).
The length of CD is 8-%28-3%29=8%2B3=11 .
Since opposite sides are congruent and parallel, ABCD is a parallelogram.
Since the x-coordinates of B and C are not the same,
BC is not part of a vertical line, and therefore is not perpendicular to AB or CD.
Since not all the angles are right angles, ABCD is not a rectangle.
The length of BC is calculated from the coordinates of B and C as
.
Since the length of BC is not the same as the lengths of AB and CD, it is not a rhombus.