Question

Question 4
If in two triangles $\Delta ABCand\Delta PQR,\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$, then

(A) $\Delta PQR\sim \Delta CAB$
(B) $\Delta PQR\sim \Delta ABC$
(C) $\Delta CBA\sim \Delta PQR$
(D) $\Delta BCA\sim \Delta PQR$

Answer 1

(A) $\Delta PQR\sim \Delta CAB$

Given that in $\Delta ABCand\Delta PQR,\frac{AB}{QR}=\frac{BC}{PR}=\frac{CA}{PQ}$.This shows that sides of one triangle are proportional to the sides of the other triangle.
If the sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are also equal. So by SSS similarity rule, the given triangles are similar.
i.e., $\Delta CAB\sim \Delta PQR$