Question

ABCD is a trapezium in which AB || DC and AB > CD. If EF is its median and X, Y are mid-points of its diagonals, then the value of

Answer 1

Given :  ABCD is a trapezium in which AB || DC and AB > CD.  

EF is its median and

X, Y are mid-points of its diagonals,  

To Find :  the value of  (EF + XY)/(EF - XY)

Solution:

line joining the mid-point of two sides of a triangle is equal to half the length of the third side and parallel to 3rd side.

EF is its median

=> AB || CD || EF

EF = (1/2)(AB + CD)

X, Y are mid-points of its diagonals,  

Hence EX  = (1/2) CD   EY = (1/2)AB

XY = EY - EX = (1/2)( AB -  CD)

EF + XY  =  (1/2)(AB + CD) + (1/2)( AB -  CD)  = AB

EF - XY =    (1/2)(AB + CD) - (1/2)( AB -  CD)  =  CD

Hence  value of (EF + XY)/(EF - XY)  is  AB/CD

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