Question

In triangles $ABC$ and $PQR$, $\angle A=\angle Q$ and $\angle B=\angle R$. Which side of $△PQR$ should be equal to side $AB$ of $△ABC$ so that the two triangles are congruent? Give reason for your answer.

Answer 1

Identify the required side:

Given that, in triangles $ABC$ and $PQR$, $\angle A=\angle Q$ and $\angle B=\angle R$

In $△ABC$ we can observe that side $AB$ is the included side between two angles $\angle A$ and $\angle B$.

Similarly in $△PQR$ we can observe that side $QR$ is the included side between two angles $\angle Q$ and $\angle R$.

According to the $ASA$( angle included side angle) congruence rule, two triangles are said to be congruent if any two angles and the included side between them of a triangle are equal to the corresponding angles and included side between them of the other triangle.

Hence, for $△PQR$ to be congruent with $△ABC$, the side $QR$ must be equal to side $AB$.

Therefore, side $QR$ of $△PQR$ should be equal to side $AB$ of $△ABC$.