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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 triangles $\text{ABC}$ and $\text{DEF}, \frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FD}},$ then they will be similar, when :
  • A
    $\angle\text{B}=\angle\text{E}$
  • B
    $\angle\text{A}=\angle\text{D}$
  • ✓
    $\angle\text{B}=\angle\text{D}$
  • D
    $\angle\text{A}=\angle\text{F}$
✓

Answer

Correct option: C.
$\angle\text{B}=\angle\text{D}$
Given, in $\triangle\text{ABC}$ and $\triangle\text{DEF},$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{FD}}$

Here, Angle formed by $DE$ and $FD$ is $\angle\text{D}.$
So, $\angle\text{B}=\angle\text{D}$
$\Rightarrow\text{DABC}\sim\text{DEDF}$

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