If AB = QR, BC = PR

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

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