Answer :

(i) OB = OD


OB = OD [In a parallelogram diagonals bisect each other]


(ii) OBY =ODX [Alternate interior angles are equal]


(iii) BOY= DOX [Vertically opposite angles are equal]


(iv) ΔBOY ΔDOX


In ΔBOY and ΔDOX


OB = OD [In a parallelogram diagonals bisect each other]


OBY =ODX [Alternate interior angles are equal]


BOY= DOX [Vertically opposite angles are equal]


ΔBOY ΔDOX [ASA rule]


Now, state if XY is bisected at O.


Hence OX = OY [Corresponding parts of congruent triangles]


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