question_answer

  If \[\Delta ABC\tilde{\ }\Delta EDF\] and \[\Delta ABC\] is not similar to\[\Delta DEF,\]the which of the following is not true?    

A) \[\text{BC}.\text{EF}=\text{AC}.\text{FD}\]

B) \[AB.\text{EF}=\text{AC}.\text{DE}\]

C) \[\text{BC}\text{.DE}=\text{AB}.\text{EF}\]

D) \[\text{BC}\text{.DE}=\text{AB}.\text{FD}\]

Correct Answer: C

Solution :

[c] Given. \[\Delta ABC\tilde{\ }\Delta EDF\]

\[\therefore \,\,\,\,\,\,\,\,\frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{EF}\]

Taking first two terms,

we get \[\frac{AB}{ED}=\frac{BC}{DF}\]

\[\Rightarrow \,\,AB\cdot DF=ED\cdot BC\] or \[BC\cdot DE=AB\cdot FD\]

So, option [d] is true.

Taking last two terms, we get

\[\frac{BC}{DF}=\frac{AC}{EF}\,\,\,\,\,\,\,\,\,\,\,\Rightarrow \,\,BC\cdot EF=AC\cdot DF\]

So. option [a] is true.

Taking first and last terms, we get

\[\frac{AB}{ED}=\frac{AC}{EF}\,\,\,\,\,\,\,\Rightarrow \,\,\,\,AB\cdot EF=ED\cdot AC\]

Hence, option [b] is true.