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# Not sure where to start here...

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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

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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
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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