Question

From the following data, state if $△ABC\sim △DEF$ or not.
$\angle B={65}^o,\angle C={82}^o,\angle D={33}^o,\angle F={65}^o$

Answer 1

In $△ABC,\angle B={65}^o,\angle C={82}^o$
$\therefore \angle A={180}^o-({65}^o+{82}^o)={180}^o-{147}^o={33}^o$
In $△DEF,\angle D={33}^o,\angle F={65}^o$
$\therefore \angle E={180}^o-({33}^o+{65}^o)={180}^o-{98}^o={82}^o$
$\therefore \angle A=\angle D,\angle B=\angle F$ and $\angle C=\angle E$
$\Rightarrow △ABC\sim △DEF$