Question

Question 3
If $\Delta ABC\sim \Delta EDFand\Delta ABC$ is not similar to $\Delta DEF$, 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

(C) BC.DE = AB.EF

Given, $\Delta ABC\sim \Delta EDF$
$\therefore \frac{AB}{ED}=\frac{BC}{DF}=\frac{AC}{EF}$


Taking first two terms, we get
$\frac{AB}{ED}=\frac{BC}{DF}$
$\Rightarrow AB.DF=BC.ED$
Or BC.DE = AB.FD

Taking last two terms, we get
$\frac{BC}{DF}=\frac{AC}{EF}$
$\Rightarrow BC.EF=AC.DF$
Or BC.EF = AC.FD

Taking first and last terms, we get
$\frac{AB}{ED}=\frac{AC}{EF}$
$\Rightarrow AB.EF=AC.ED$
Or AB.EF = AC.DE