Question

Question 2
If AB = QR, BC+PR and CA = PQ, then
(A) $\Delta ABC\cong \Delta PQR$
(B) $\Delta CBA\cong \Delta PQR$
(C) $\Delta BAC\cong \Delta BCA$
(D) $\Delta PQR\cong \Delta BCA$

Answer 1

We know that, if $\Delta RST$ is congruent to $\Delta UVM$ i.e., $\Delta RST\cong \Delta UVW$, then sides of $\Delta RST$ fall on corresponding equal sides of $\Delta UVW$ and angles of $\Delta RST$ fall on corresponding equal angles of $\Delta UVW$

Here, given AB = QR, BC = PR and CA = PQ, which shows that AB covers QR, BC covers PR and CA covers PQ i.e., A correspond to Q, B correspond to R and C correspond to P
Or $A\leftrightarrow Q,B\leftrightarrow R,C\leftrightarrow P$
$\Delta ABC=\Delta QRP$, so option (a) is incorrect
or $\Delta BAC\cong \Delta RQP$, so option (c) is incorrect
or $\Delta CBA\cong \Delta PRQ$, so option (b) is correct
or $\Delta BCA\cong \Delta RPQ$. So option (d) is incorrect.