MCQ
Choose the correct answer from the given four options:
If in two triangles DEF and PQR, $\angle\text{D}=\angle\text{Q}\ \text{and}\ \angle\text{R}=\angle\text{E},$ then which of the following is not true?
  • A
    $\frac{\text{EF}}{\text{PR}}=\frac{\text{DF}}{\text{PQ}}$
  • $\frac{\text{DF}}{\text{PQ}}=\frac{\text{EF}}{\text{RP}}$
  • C
    $\frac{\text{DF}}{\text{QR}}=\frac{\text{DF}}{\text{PQ}}$
  • D
    $\frac{\text{EF}}{\text{RP}}=\frac{\text{DF}}{\text{RQ}}$

Answer

Correct option: B.
$\frac{\text{DF}}{\text{PQ}}=\frac{\text{EF}}{\text{RP}}$
Give, $\triangle\text{DEF},\angle\text{D}=\angle\text{Q},\angle\text{R}=\angle\text{E}$

$\therefore\triangle\text{DEF}\sim\triangle\text{QRP}$ [by AAA similarity criterion]
$\Rightarrow\angle\text{F}=\angle\text{P}$ [Corresponding angles of similar triangles]
$\therefore\frac{\text{DF}}{\text{PQ}}=\frac{\text{EF}}{\text{RP}}$ Hence proved.

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