In Fig. diagonals \( \mathrm{AC} \) and \( \mathrm{BD} \) of quadrilateral \( \mathrm{ABCD} \) i...

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In Fig. diagonals \( \mathrm{AC} \) and \( \mathrm{BD} \) of quadrilateral \( \mathrm{ABCD} \) intersect at \( \mathrm{O} \) such that \( \mathrm{OB}=\mathrm{OD} \). If \( \mathrm{AB}=\mathrm{CD} \), then show that:
(i) \( \operatorname{ar}(\mathrm{DOC})=\operatorname{ar}(\mathrm{AOB}) \)
- (ii) \( \operatorname{ar}(\mathrm{DCB})=\operatorname{ar}(\mathrm{ACB}) \)
- (iii) DA\|l CB or ABCD is a parallelogram.
[Hint: From D and B, draw perpendiculars to \( \mathrm{AC} \).]
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