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class-10
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Answer:
Quadrilateral ABCD is a trapezium......given
segAB ll segDC.
therefore,angle ABD congruent angle CDB.....by Alternate angles
i.e. angle ABO congruent angle CDO.....(1)...(B-O-D)
In triangle AOB and triangle COD,
angle ABO congruent angle CDO...from (1)
angle AOB congruent angle COD.... by vertically opposite angles.
Therefore,triangle AOB similar triangle COD.......by AA test of similarity.
Therefore, OA/OC=OB/OD.......by Corresponding sides of similar triangle.