NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 6: Triangles - Exercise 6.1

Question 4

Step 1: In the question, we are given that the sides of the two triangles are in the same ratio:

\(\dfrac{AB}{QR} = \dfrac{BC}{PR} = \dfrac{CA}{PQ}\).

Step 2: For similarity of triangles (by the SSS similarity criterion), the three sides of one triangle must be proportional to the three sides of another triangle.

Step 3: Compare the sides:

• \(AB\) in triangle ABC corresponds to \(QR\) in triangle PQR.
• \(BC\) in triangle ABC corresponds to \(PR\) in triangle PQR.
• \(CA\) in triangle ABC corresponds to \(PQ\) in triangle PQR.

Step 4: Now, write down the order of the vertices according to this correspondence:

\(A \rightarrow Q,\; B \rightarrow R,\; C \rightarrow P\).

Step 5: So the triangle \(BCA\) in the first triangle matches with \(PQR\) in the second triangle.

Final Answer: \(\triangle BCA \sim \triangle PQR\).