Question

In $△ABC,\angle A={90}^o$ & $\angle B={30}^o$. In $△DEF,\angle E={30}^o$ & $\angle F={60}^o$.

Are triangles similar & if yes, name the similarlty criteria?

• A. $AAS$
• B. $AAA$
• C. $SSS$
• D. $SAS$

Answer 1

The correct option is B $AAA$

In $\Delta DEF$ by angle sum property,
$\angle D={180}^o-{30}^o-{60}^o$

$\angle D={90}^o$

$\angle A=\angle D$

$\angle B=\angle E$
By using angle sum property for $\Delta ABC,$

$\angle C={60}^o$

Also, $\angle C=\angle F$
Triangles are similar by $AAA$ similarity.

$ABC\sim DEF$