Question

In triangles ABC and PQR, if AB = QR,
BC = RP, and CA = PQ, then which of the following holds?

• A. $\Delta ABC\cong \Delta PQR$
• B. $\Delta CBA\cong \Delta PQR$
• C. $\Delta CAB\cong \Delta PQR$
• D. $\Delta BCA\cong \Delta PQR$

Answer 1

The correct option is C $\Delta CAB\cong \Delta PQR$

We know that if two triangles are congruent, then their corresponding sides are equal, and vice-versa.

Here,
AB = QR, (given) --- (1)
BC = RP, (given) --- (2)
CA = PQ (given) --- (3)

From (2) and (3), vertex P corresponds to vertex C.
From (1) and (3), vertex Q corresponds to vertex A.
From (1) and (2), vertex R corresponds to vertex B.

∴ ∆CAB ≅ ∆PQR (By SSS congruency)