Question:
If AB = QR, BC = PR and CA = PQ, then
(a) ΔABC ≅ ΔQRP
(b) ΔCBA ≅ ΔPRQ
(c) ΔBAC ≅ ΔRQP
(d) ΔPQR ≅ ΔBCA
Solution:
(b) We know that, if ΔRST is congruent to ΔUVW i.e., ΔRST = ΔUVW, then sides of ΔRST fall on corresponding equal sides of ΔUVW and angles
of ΔRST fall on corresponding equal angles of ΔUVW.
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↔Q,B↔R,C↔P
Under this correspondence,
ΔABC ≅ ΔQRP, so option (a) is incorrect,
or ΔBAC ≅ ΔRQP, so option (c) is incorrect,
or ΔCBA ≅ ΔPRQ, so option (b) is correct,
or ΔBCA ≅ ΔRPQ, so option (d) is incorrect