When given the information below, can you conclude that Quadrilateral WXYZ is a parallelogram? Why or why not?

In Quadrilateral WXYZ, the sides have the following slopes:
WX: m = 1/3
XY: m = -3
YZ: m = -3
WZ: m = 1/3
A) No, because opposite sides are not congruent
B) No, because opposite sides are not parallel
C) Yes, because opposite sides are congruent
D) Yes, because opposite sides are parallel

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absor201 absor201 · Answer 1 · 2020-02-09T13:47:54+01:00

The right answer is: "B) No, because opposite sides are not parallel"

Step-by-step explanation:

Given

Quadrilateral WXYZ

If the given quadrilateral is a parallelogram the slopes of opposite sides will be equal as the opposite sides should be parallel

Hence the slopes of WX and YZ should be equal and the slopes of XY and WZ should be equal

while we can see that the slopes of opposite sides are not same.

[tex]Slope\ of\ WX \neq Slope\ of\ YZ\\\frac{1}{3} \neq -3\\Similarly,\\Slope\ of\ XY \neq Slope\ of\ WZ\\-3 \neq \frac{1}{3}[/tex]

So it is not a parallelogram.

Hence,

The right answer is: "B) No, because opposite sides are not parallel"

Keywords: Shapes, slopes

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