SOLUTION: Prove that the quadrilateral formed by connecting the midpoints of the sides of quadrilateral ABCD is a parallelogram.

Algebra ->  Parallelograms -> SOLUTION: Prove that the quadrilateral formed by connecting the midpoints of the sides of quadrilateral ABCD is a parallelogram.      Log On


   

Question 1139131: Prove that the quadrilateral formed by connecting the midpoints of the sides of quadrilateral ABCD is a parallelogram.
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.

See the lesson
    - Midpoints of a quadrilateral are vertices of the parallelogram
in this site and find the proof there.

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

The referred lesson is 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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I do not understand why Edwin in his post does instruct you to write "two-column proof" - the problem in the post does not require it . . .

So, you may ignore this his instruction.



Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


All you need do is to draw one diagonal, say, PR.

 

Then AD is a midline of triangle PRS and thus parallel to and half
the length of PR. 

Similarly, BC is a midline of triangle PRQ and is 
thus ALSO parallel to and half the length of PR.  So AD and BC are both>
parallel and equal in length.  That's enough to prove ABCD is a 
parallelogram.  Now go write that up in a two-column proof.

Edwin