Question

In triangles $\mathrm{ABC}$ and $\mathrm{PQR}$, $\angle \mathrm{A}=\angle \mathrm{Q}$ and $\angle \mathrm{B}=\angle \mathrm{R}$.

Which side of $△\mathrm{PQR}$ should be equal to side $\mathrm{BC}$ of $△\mathrm{ABC}$ so that the two triangles are congruent.

Answer 1

Find the required pair of sides.

In the question, it is given that in triangles $\mathrm{ABC}$ and $\mathrm{PQR}$, $\angle \mathrm{A}=\angle \mathrm{Q}$ and $\angle \mathrm{B}=\angle \mathrm{R}$.

If $\mathrm{BC}=\mathrm{PR}$ then by $\mathrm{AAS}$, $△\mathrm{ABC}\cong △\mathrm{PQR}$

Hence $\mathrm{BC}=\mathrm{PR}$ for $△\mathrm{PQR}$ and $△\mathrm{ABC}$ to be congruent.