Question

If AB = QR, BC = PR and CA = PQ, then ______.

Options

• ∆ABC ≅ ∆PQR

• ∆CBA ≅ ∆PRQ

• ∆BAC ≅ ∆RPQ

• ∆PQR ≅ ∆BCA

Answer 1

If AB = QR, BC = PR and CA = PQ, then ∆CBA ≅ ∆PRQ.

Explanation:

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 ΔCBA ≅ ΔPRQ, so option (b) is correct,

or ΔBAC ≅ ΔRQP, so option (c) is incorrect,

or ΔBCA ≅ ΔRPQ, so option (d) is incorrect.