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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
Choose the correct answer from the given four options : If in two traingles $\text{ABC}$ and $\text{PQR},$
$\frac{\text{AB}}{\text{QR}}=\frac{\text{BC}}{\text{PR}}=\frac{\text{CA}}{\text{PQ}},$ then :
  • A
    $\triangle\text{PQR}\sim\triangle\text{CAB}$
  • B
    $\triangle\text{PQR}\sim\triangle\text{ABC}$
  • ✓
    $\triangle\text{CBA}\sim\triangle\text{PQR}$
  • D
    $\triangle\text{BCA}\sim\triangle\text{PQR}$
✓

Answer

Correct option: C.
$\triangle\text{CBA}\sim\triangle\text{PQR}$
Given, in two $\triangle\text{PQR}=\frac{\text{AB}}{\text{QR}}=\frac{\text{BC}}{\text{PR}}=\frac{\text{CA}}{\text{PQ}} $
Which shows that sidles of one triangle are proportional to the side of thew other triangle,
then their Corresponding angles are also equal, so by $\text{SSS}$ similarity, triangles are similar.
$\text{i.e.,}\ \triangle\text{CAB}\sim\triangle\text{PQR}$​​​​​​​

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