Pls answer no 13

Dear Student ,

Please find below the solution to the asked query :

$$\begin{gathered} 13. \\ \left(\mathrm{i}\right) \mathrm{Yes}, \\ \mathrm{RB}=\mathrm{OM} \\ \mathrm{Since} \mathrm{opposite} \mathrm{sides} \mathrm{of} \mathrm{a} \mathrm{rectangle} \mathrm{are} \mathrm{equal}. \\ \left(\mathrm{ii}\right) \mathrm{Yes}, \\ \angle \mathrm{MYO} = \angle \mathrm{RXB} \\ \mathrm{Since} \mathrm{each} \mathrm{angle} \mathrm{is} 90° \mathrm{as} \mathrm{MY} \mathrm{and} \mathrm{RX} \mathrm{are} \mathrm{perpendiculars}. \\ \left(\mathrm{iii}\right) \mathrm{Yes}, \\ \angle \mathrm{MOY} = \angle \mathrm{RBX} \\ \mathrm{Since} \mathrm{both} \mathrm{are} \mathrm{alternate} \mathrm{interior} \mathrm{angles} \mathrm{as} \mathrm{MO} \parallel \mathrm{BR}. \\ \left(\mathrm{iv}\right) \mathrm{Yes} \\ \mathrm{In} △\mathrm{MYO} \mathrm{and} △\mathrm{RXB} \\ \mathrm{RB}=\mathrm{OM} \\ \angle \mathrm{MYO} = \angle \mathrm{RXB} \\ \angle \mathrm{MOY} = \angle \mathrm{RBX} \\ \mathrm{By} \mathrm{AAS} \mathrm{criterion}, \\ △\mathrm{MYO} \cong △\mathrm{RXB} \\ \left(\mathrm{v}\right) \mathrm{Yes}, \\ \mathrm{MY} = \mathrm{RX} \left( \mathrm{CPCT} \right). \end{gathered}$$

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