Question

In the adjoining figure, two triangles are given.

Which of the following is correct?

• A. $△ABC\cong △PQR$
• B. $△ABC\cong △PRQ$
• C. (a) and (b) above.
• D. None of the above

Answer 1

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

In $△ABC$
$m\angle A={180}^o-m\angle B-\angle Cm\angle A={180}^o-{80}^o-{40}^o={60}^o$

In $△PQR$
$m\angle Q={180}^o-m\angle P-\angle Rm\angle Q={180}^o-{60}^o-{80}^o={40}^o$

Hence,
$\bullet$ $m\angle A=m\angle P={60}^o$
$\bullet$ $m\angle B=m\angle R={80}^o$
$\bullet$ $m\angle C=m\angle Q={40}^o$

$\underset{–}{\text{Note}}$: Congruent triangles are named by listing their vertices in corresponding orders.

$\bullet A$ corresponds to $P$
$\bullet B$ corresponds to $R$
$\bullet C$ corresponds to $Q$

Hence, $△ABC\cong △PRQ$

So, option(b.) is correct.