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In Fig. \( \quad A B C \) is a right triangle right angled at \( A . B C E D, A C F G \) and \( A B M N \) are squares on the sides \( \mathrm{BC}, \mathrm{CA} \) and \( \mathrm{AB} \) respectively. Line segment \( \mathrm{AX} \perp \mathrm{DE} \) meets \( \mathrm{BC} \) at Y. Show that:
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(i) \( \triangle \mathrm{MBC} \cong \triangle \mathrm{ABD} \)
(ii) \( \operatorname{ar}(\mathrm{BYXD})=2 \operatorname{ar}(\mathrm{MBC}) \)
(iii) \( \operatorname{ar}(\mathrm{BYXD})=\operatorname{ar}(\mathrm{ABMN}) \)
(iv) \( \triangle \mathrm{FCB} \cong \triangle \mathrm{ACE} \)
(v) \( \operatorname{ar}(\mathrm{CYXE})=2 \) ar \( (\mathrm{FCB}) \)
(vi) \( \operatorname{ar}( \) CYXE) \( =\operatorname{ar}(\mathrm{ACFG}) \)
(vii) \( \operatorname{ar}(\mathrm{BCED})=\operatorname{ar}(\mathrm{ABMN})+\operatorname{ar}(\mathrm{ACFG}) \)
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