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Triangles — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
If in two triangles $\text{ABC}$ and $\text{DEF,} \frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FE}}=\frac{\text{CA}}{\text{FD}},$ then:
  • ✓
    $\triangle\text{FDE}\sim\triangle\text{CAB}$
  • B
    $\triangle\text{FDE}\sim\triangle\text{ABC}$
  • C
    $\triangle\text{CBA}\sim\triangle\text{FDE}$
  • D
    $\triangle\text{BCA}\sim\triangle\text{FDE}$
✓

Answer

Correct option: A.
$\triangle\text{FDE}\sim\triangle\text{CAB}$

In $\triangle\text{ABC}$ and $\triangle\text{DEF,}$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FE}}=\frac{\text{CA}}{\text{FD}} ($By $\text{SSS}$ axiom$)$
$\therefore\triangle\text{FDE}=\triangle\text{CAB}$

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