Question 1197664
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Hi, can you help me solve this problem?
Given a quadrilateral whose vertices are ( 3, 5 ) , ( 4, -1 ), ( 8, -2 ) and ( 9, 7 ), show
that the line segments joining the midpoints of adjacent sides from a parallelogram.
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<pre>
This statement is true for ANY convex quadrilateral on a plane:


    for any convex quadrilateral on a plane, the segments joining
    the midpoints of adjacent sides form a parallelogram.


The proof is in couple of lines.


    Draw one diagonal of the parallelogram.

    Then two of the four listed segments are midlines in the two triangles.
    Therefore, these two segments are parallel to that diagonal and,
    hence, are parallel to each other.


    Same reasoning works for other two segments and the other diagonal.


    Thus, these segments are in-pair parallel as opposite sides 
    of the drawn quadrilateral, proving that the drawn quadrilateral,
    consisting of these segments is a parallelogram.
</pre>

The statement is proved and the proof is completed.


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See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/Midpoints-of-a-quadrilateral-are-vertices-of-the-parallelogram.lesson>Midpoints of a quadrilateral are vertices of the 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 lesson is the part of this online textbook under the topic &nbsp;"<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.