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Triangles — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsTriangles1 Mark
MCQ
Choose the correct answer from the given four options:
$\text{If}\ \triangle\text{ABC}\sim\triangle\text{EDF}\text{ and}\ \triangle\text{ABC}$ is not similar to $\triangle\text{DEF},$ then which of the following is not true?
  • A
    BC × EF = AC × FD
  • ✓
    AB × EF = AC × DE
  • C
    BC × DE = AB × EF
  • D
    BC × DE = AB × FD
✓

Answer

Correct option: B.
AB × EF = AC × DE
Given, $\triangle\text{ABC}\sim\triangle\text{EDF}$
$\therefore\ \frac{\text{AB}}{\text{ED}}=\frac{\text{BC}}{\text{DF}}=\frac{\text{AC}}{\text{EF}}$

Taking first two terms, we get
$\frac{\text{AB}}{\text{ED}}=\frac{\text{BC}}{\text{DF}}$
$\Rightarrow\text{AB}\times\text{DF}=\text{ED}\times\text{BC}$
$\text{or}\ \text{BC}\times \text{DE}=\text{AB}\times\text{DF}$
So, option (a) is also true.
Taking first and last terms, we get
$\frac{\text{BC}}{\text{DF}}=\frac{\text{AC}}{\text{EF}}$
$\Rightarrow\text{AB}\times\text{EF} = \text{ED}\times\text{AC}$
Hence, Option (b) is true.

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