Question

Which similarity criterion is used for the given triangles?

• A. AA
• B. SAS
• C. SSS
• D. AAA

Answer 1

The correct option is D AAA

In $△ABC$ using angle sum property,

$\angle A+\angle B+\angle C={180}^{\circ }{50}^{\circ }+{70}^{\circ }+\angle C={180}^{\circ }\Rightarrow \angle C={60}^{\circ }$

Similarly in $△PQR$,

$\angle P+\angle Q+\angle R={180}^{\circ }{50}^{\circ }+\angle Q+{60}^{\circ }={180}^{\circ }\Rightarrow \angle Q={70}^{\circ }$

Now in$△ABC$ and $△PQR$,

$\angle A=\angle P$

$\angle B=\angle Q$

$\angle C=\angle R$

So, $△ABC\sim △PQR$ by $AAA$ criteria