Question : In a $\triangle \mathrm{PQR}$ and $\triangle\mathrm{ABC}$, $\angle$P = $\angle$A and AC = PR. Which of the following conditions is true for $\triangle$PQR and $\triangle$ABC to be congruent?
Option 1: AB = PQ by SSS
Option 2: AB = PQ by SAS
Option 3: BC = QR by ASS
Option 4: $\angle$Q = $\angle$B by AAA
Correct Answer: AB = PQ by SAS
Solution :
In a $\triangle \mathrm{PQR}$ and $\triangle \mathrm{ABC}$,
$\angle$P = $\angle$A
AC = PR
For triangle PQR and ABC to be congruent if AB = PQ then they will be congruent by SAS rule.
Hence, the correct answer is AB = PQ by SAS.
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