Question
In the given figure,
$AB || DC$ prove that
$\triangle\text{DMU}\sim\triangle\text{BMV}$
$AB || DC$ prove that
$\triangle\text{DMU}\sim\triangle\text{BMV}$
✓
Answer
Given, $AB || DC$
In triangle $DMU$ and $BMV$, we have
$\angle\text{MUD}=\angle\text{MVB}$
Each angle is equal to $90^\circ $
$\angle\text{UMD}=\angle\text{VMB}$
Each are vertically opposite angles.
Therefore, by $AA-$criterion of similarity $\triangle\text{DMU}\sim\triangle\text{BMV}$
In triangle $DMU$ and $BMV$, we have
$\angle\text{MUD}=\angle\text{MVB}$
Each angle is equal to $90^\circ $
$\angle\text{UMD}=\angle\text{VMB}$
Each are vertically opposite angles.
Therefore, by $AA-$criterion of similarity $\triangle\text{DMU}\sim\triangle\text{BMV}$
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