Question

In $△ABC$ and $△PQR,\angle A={30}^o,\angle B={70}^o,\angle P={70}^o,\angle Q={80}^o$ and $AB=RP,$ then

• A. $△ABC\cong △PQR$
• B. $△ABC\cong △QRP$
• C. $△ABC\cong △RPQ$
• D. $△ABC\cong △PRQ$

Answer 1

The correct option is D $△ABC\cong △PRQ$

In $△ABC,\angle A={30}^o,\angle B={70}^o$
$\angle C={180}^o-(\angle A+\angle B)$
[Angle sum property of triangle]
$\angle C={180}^o-({30}^o+{70}^o)$
$\angle C={80}^o$

In $△PQR,\angle P={70}^o,\angle Q={80}^o$
So, $\angle R={180}^o-(\angle P+\angle Q)$ [Angle sum property of triangle]
$\angle R={180}^o-({70}^o+{80}^o)$
$\angle R={30}^o$

In the $△ABC$ and $△PQR,$ we have
$\angle C=\angle Q$
$\angle A=\angle P$
$AB=PR$ [Given]
$\therefore △ABC\cong △PRQ$ [By AAS congruence]