Question 1187857
.


            Unfortunately,  the arguments in the post by  @MathLover1 are not correct.


            We are not given that the opposite sides are parallel,  so we  CAN  NOT  use it as an argument.



<pre>
What is TRUE, it is that the opposite sides have equal length at the given values of x and y, and you can check it on your own,

by substituting x = 5  and  y = 8  into the formulas.


This fact is just enough to state that the quadrilateral is a parallelogram,


BECAUSE every quadrilateral with congruent opposite sides is a parallelogram.
</pre>


Regarding this last my statement, it is actually one of Theorems of Geometry, related to parallelograms.



See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-the-sides-of-a-parallelogram.lesson>Properties of the sides of a parallelogram</A> 

in this site.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part of this textbook under the topic "<U>Properties of parallelograms</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson


to your archive and use it when it is needed.