Question

If $△ABC\sim △EDF$ and $△ABC$ is not similar to $△DEF,$ then which of the following is not true?

• A. $BC.EF=AC.FD$
• B. $AB.EF=AC.DE$
• C. $BC.DE=AB.EF$
• D. $BC.DE=AB.FD$

Answer 1

The correct option is C $BC.DE=AB.EF$

If $△ABC\sim △EDF,$ then
$\frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{EF}$
$\therefore$ $\frac{AB}{ED}=\frac{BC}{DF}\Rightarrow AB\times DF=BC\times ED$
$\frac{BC}{DF}=\frac{AC}{EF}\Rightarrow BC\times EF=AC\times DF$
$\frac{AB}{ED}=\frac{AC}{EF}\Rightarrow AB\times EF=AC\times ED$
$\therefore$ $BC\times DE\ne AB\times EF$