Quadrilateral PQRS is a trapezoid with bases PQ and RS. The median MN meets the diagonals PQ and RS at X and Y, respectively. If SR=20 and XY=5, find PQ.
+128475 Let Z be the intersection point of the diagonals
And note that triangle XYZ is similar to triangle RZS
So since RS = 20 and XY = 5, the height of triangle RZS is 4 times that of the height of triangle XYZ
So....there are 5 equal parts of the distance from SR to the midline
And one of these parts is the height of triangle XYZ
And 4 of the parts = the height of triangle RZS
And triangle PZQ is similar to triangle RZS
And there are also 5 of the same equal parts from PQ to the midline
And so there are 6 equal parts to the height of triangle PZQ....the 5equal parts to the midline and the one other equal part of the height of triangle XYZ
So.....the height of triangle PZQ to the height of triangle RZS = 6/4 = 3/2
So....the base of triangle PZQ = (3/2) the base of triangle RZS = (3/2) 20 = 30 = PQ
