Question

Assertion (A): In $$\triangle ABC$$ and $$\triangle PQR$$, if $$\frac{AB}{QR} = \frac{BC}{PR} = \frac{CA}{PQ}$$ then $$\triangle ABC\sim\triangle PQR$$.

Reason (R): If the corresponding sides of two triangles are proportional then the triangles are similar.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is false and Reason (R) is true.

Explanation:

Step 1 – Assertion: A is false. The given side ratios pair $$AB$$ with $$QR$$, $$BC$$ with $$PR$$ and $$CA$$ with $$PQ$$. These correspond to the vertex order $$\triangle ABC\sim\triangle QRP$$, not $$\triangle PQR$$.

Step 2 – Reason: R is true. If corresponding sides are proportional, the triangles are similar by the SSS criterion.