MCQ
If in two $\triangle\text{ABC}$ and $\text{PQR},\frac{\text{AB}}{\text{QR}} =\frac{\text{BC}}{\text{PR}}=\frac{\text{CA}}{\text{PQ}},$ then,
  • $\triangle{\text{PQR}}\sim\triangle\text{CAB}$
  • B
    $\triangle{\text{PQR}}\sim\triangle\text{ABC}$
  • C
    $\triangle{\text{CBA}}\sim\triangle\text{PQR}$
  • D
    $\triangle{\text{BCA}}\sim\triangle\text{PQR}$

Answer

Correct option: A.
$\triangle{\text{PQR}}\sim\triangle\text{CAB}$
Given that, If in two $\triangle\text{ABC}$ and $\text{PQR},$
$\frac{\text{AB}}{\text{QR}} =\frac{\text{BC}}{\text{PR}}=\frac{\text{CA}}{\text{PQ}}$
If sides of one triangle are proportional to the side of the other triangle, and their corresponding angles are also equal, then both the triangles are similar by $\text{SSS}$ similarity.
$\therefore\triangle\text{PQR}\sim \text{CAB}$

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