question_answer

If in two triangles ABC and PQR, \[\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ},\] then: (NCERT EXEMPLAR)

A) \[\Delta PQR\tilde{\ }\Delta CAB\]

B) \[\Delta PQR\tilde{\ }\Delta ABC\]

C) \[\Delta CBA\tilde{\ }\Delta PQR\]

D) \[\Delta BCA\tilde{\ }\Delta PQR\]

Correct Answer: A

Solution :

[a] Given, in triangles ARC and PQR, \[\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ},\]which shows that sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are also equal, so by SSS similarity, triangles are similar, i.e., \[\Delta CAB\tilde{\ }\Delta PQR.\]