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Quadrilateral \(PQRS\) is a trapezoid with bases \(\overline{PQ}\) and \(\overline{RS}\). The median \(\overline{MN}\) meets the diagonals \(\overline{PR}\) and \(\overline{QS}\) at \(X\) and \(Y\), respectively. If \(SR = 20\) and \(XY = 7\), find \(PQ\).

 

Thank you so much for helping me!

 May 25, 2020
 #1
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Look at triangle(SPR):

--  MX is a midline of this triangle, so its length is one-half the length of the base, SR:

    MX  =  10

 

Look at triangle(RSQ)

--  YN is a midline of this triangle, so its length is one-half the length of the base, SR:

    YN  =  10

 

Now look at MN

--  MN  =  MY + XY + YN   --->   MN  =  10 + 7 + 10  =  27

 

To find PQ:

--  MN must have a value half-ways between SR and PQ.

--  MN = 27,  SR = 20   --->   PQ  =  34

 May 25, 2020
 #2
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I understand it now. Thank you again!

 May 25, 2020

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