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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
If $\triangle\text{ABC}\sim\triangle\text{EDF}$ and $\triangle\text{ABC}$ is not similar to $\triangle\text{DEF}$ then which of the following is not true?
  • A
    $\text{BC}\cdot\text{EF}=\text{AC}\cdot\text{FD}$
  • B
    $\text{AB}\cdot\text{EF}=\text{AC}\cdot\text{DE}$
  • ✓
    $\text{BC}\cdot\text{DE}=\text{AB}\cdot\text{EF}$
  • D
    $\text{BC}\cdot\text{DE}=\text{AB}\cdot\text{FD}$
✓

Answer

Correct option: C.
$\text{BC}\cdot\text{DE}=\text{AB}\cdot\text{EF}$
In $\triangle\text{ABC}\sim\triangle\text{EDF},$ but $\triangle\text{ABC}$ is not similar $\triangle\text{DEF}.$
Since $\triangle\text{ABC}\sim\triangle\text{EDF},$
$\Rightarrow\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{DF}}=\frac{\text{AC}}{\text{EF}}$
So, $\text{AB}\cdot\text{EF}=\text{AC}\cdot\text{DE}$
Hence, $\text{BC}\cdot\text{DE}\not=\text{AB}\cdot\text{EF}.$

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