Question

If in two $\triangle$ XYZ and $\triangle$ MNO, $\:\sf{\frac{XY}{NO}=\frac{XZ}{MO}=\frac{ZY}{MN},\:}$then: (a) $\sf{\triangle{MNO}\sim\triangle{ZXY}}$ (b) $\sf{\triangle{MNO}\sim\triangle{XYZ}}$ (c) $\sf{\triangle{ZYX}\sim\triangle{MNO}}$ (d) $\sf{\triangle{YZX}\sim\triangle{MNO}}$

Answer 1

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

• $\sf in \: \triangle \: XYZ \: and \: \triangle MNO$
• $\sf{\frac{XY}{NO}=\frac{XZ}{MO}=\frac{ZY}{MN}}$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

$\sf \purple{we \: know}$

$\sf for \: \triangle's \: \: to \: be \: similar,opposite \: sides \: should \\ \sf\: be \: in \: proportion.$

$\implies\sf XY \: (opp \: side)=NO$

$\implies \sf XZ \: (opp \: side)=MO$

$\implies \sf ZY \: (opp \: side)=MN$

$\orange{ \therefore\sf{\triangle{ZYX}\sim\triangle{MNO}}} \: \: \color{grey}{ \sf option(c)}$

HOPE IT HELPS!!