Question

If $△ABC\cong △PQR$, which of the following are correct?

• A. $m\angle A=m\angle P$
• B. $m\angle B=m\angle Q$
• C. $m\angle C=m\angle Q$
• D. $m\angle B=m\angle R$

Answer 1

Answer: (A), (B)

$m\angle B=m\angle Q$

$\text{Given:}$ $△ABC\cong △PQR$

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

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

$\because$ The triangles are congruent.
$\therefore$ The corresponding angles must be equal in measure.
$\bullet$ $m\angle A=m\angle P$
$\bullet$ $m\angle B=m\angle Q$
$\bullet$ $m\angle C=m\angle R$

Hence, options (a.) and (b.) are correct.