SOLUTION: Show that GHIJ is a parallelogram for x = 5 and y = 8. Here is a link to the image: https://imgur.com/a/WpcLFZR I have searched through my Geometry textbook multiple times and ha

Question 1187857: Show that GHIJ is a parallelogram for x = 5 and y = 8.
Here is a link to the image: https://imgur.com/a/WpcLFZR
I have searched through my Geometry textbook multiple times and have come up empty-handed. I can’t ask a teacher for help since I am homeschooled. Could you please assist me with this? I would greatly appreciate it!
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

GHIJ is parallelogram, because opposite sides are parallel and equal in length
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
.

            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.

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.

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

See the lesson
    - Properties of the sides of a parallelogram
in this site.

Also, you have this free of charge online textbook on Geometry
    GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.

The referred lessons are the part of this textbook under the topic "Properties of parallelograms".

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.

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