A quadrilateral is called a "parallelogram" if both pairs of opposite sides are parallel. Show that if WXYZ is a parallelogram, then < W = < Y and < X = < Z.  


(< = angle)


Thanks for your help!

 Jan 22, 2018
edited by AnonymousConfusedGuy  Jan 22, 2018

Let's see if I can steer you in the right direction here. If you need more assistance, just ask! Someone will probably fill you in!


As aforementioned, a parallelogram, by definition, is a quadrilateral wherein its opposite sides are parallel. Opposite angles congruency is a known property of parallelograms, but we will assume for the problem's sake that you don't know that already! Here is a simple diagram for you to reference!



I have extended the segments. Because opposite sides are parallel, this means that \(\overline{WX}\parallel\overline{ZY}\) and \(\overline{WZ}\parallel\overline{XY}\). You can start by trying to identify the relationship between angles located on the same segment (\(\angle Z\) and \(\angle Y\), for example). Then, do that process again for a segment that intersects with the segment you identified the relationship. Therefore, if you picked to compare \(\angle Z\) and \(\angle Y\), then identify the relationship between \(\angle X\) and \(\angle Y\). Use your knowledge of relations when parallel lines are involved. Once you find the relationship of these angles, see if you can relate all the information you gathered together. 


Again, I am not necessarily giving you the answer here, but I hope you will sit down and try to think this through. If you need additional help, I will be glad to give it!

 Jan 22, 2018

Thank you so much! I tried to post this yesterday but it didn't go through for some reason.  This was super helpful along with your other response. :)

AnonymousConfusedGuy  Jan 23, 2018

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