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!
+23246 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
