Question

It is given that \(\Delta ABC \sim \Delta EDF\). Which of the following is not true ?

• A. \(\frac{\text{Perimeter of } \Delta ABC}{\text{Perimeter of } \Delta EDF} = \frac{AB}{ED}\)
• B. \(\frac{AB}{ED} = \frac{AC}{EF}\)
• C. \(\angle A = \angle D, \angle C = \angle F\)
• D. \(\frac{AB + BC}{AC} = \frac{DE + DF}{EF}\)

Hint:

To avoid mistakes in similar triangle questions, write down the vertex correspondence explicitly before reading the options:
Map \(A \leftrightarrow E\), \(B \leftrightarrow D\), and \(C \leftrightarrow F\).
This simple step prevents visual confusion and helps you spot the incorrect angle mapping instantly!

Answer 1

The Correct Option is C

Step 1: Write out the vertex correspondence as a table.
$\Delta ABC \sim \Delta EDF$ tells us $A \leftrightarrow E$, $B \leftrightarrow D$, $C \leftrightarrow F$.
Step 2: Read off the true angle equalities from the table.
This correspondence gives $\angle A = \angle E$, $\angle B = \angle D$, and $\angle C = \angle F$.
Step 3: Compare each option against the table.
Option (C) claims $\angle A = \angle D$, but the table shows $\angle A$ actually equals $\angle E$, not $\angle D$. The other three options (perimeter ratio, side ratio, and the combined ratio) all follow correctly from the table.
So option (C) is the one that is not true.
\[ \boxed{\text{Option (C)}} \]