class 10th Exercise 6.2, sum no.9

                                             EXERCISE 6.2
SUM NO.9
ABCD is trapezium in which AB∥DC and its diagonals intersect each other at the point O.show that AO/BO=CO/DO.

 Solution:- 
Given:-In trapezium ABCD,AB∥DC, diagonal AC and BD intersect at o.

Construction:- Draw OE∥DC, intersecting AD at E.
Proof:- in △ ADC, OE∥DC(by construction)
   ∴ AE/ED=AO/OC......(1)

         (by Basic proportionality theorem)
Again,in △ABD,OE∥AB
AE/ED=BO/OD.....(2)
[∵ OE∥ DC (by construction) and DC∥AB (given) also by by Basic proportionality theorem)
 From (1) and (2) we have:
AO/CO=BO/OD

 AO/BO=CO/DO

 Hence proved

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