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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
If triangle $\text{ABC}$ is similar to triangle $\text{DEF},$ then,
  • A
    $\frac{\text{AB}}{\text{FD}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{DE}}$
  • B
    $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{DF}}=\frac{\text{CA}}{\text{EF}}$
  • ✓
    $\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}$
  • D
    $\frac{\text{AB}}{\text{BC}}=\frac{\text{CA}}{\text{DE}}=\frac{\text{EF}}{\text{FD}}$
✓

Answer

Correct option: C.
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}$
If two triangles are similar, i.e. when$\triangle\text{ABC}\sim\triangle\text{DEF}$, then
$(i)$ their corresponding angles are equal and
$\angle\text{A}=\angle\text{D},\angle\text{B}=\angle\text{E},\angle\text{C}=\angle\text{F}$ and
$(ii)$ their corresponding sides are in the same ratio $($or proportion$).$
$\frac{\text{AB}}{\text{DE}}=\frac{\text{BC}}{\text{EF}}=\frac{\text{CA}}{\text{FD}}$

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