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 visual confusion in similar triangle problems, always write down the vertex mapping explicitly:
Map \(A \leftrightarrow E\), \(B \leftrightarrow D\), and \(C \leftrightarrow F\) immediately.
This simple step prevents mistakes when identifying corresponding angles and side ratios!

Answer 1

The Correct Option is C

Step 1: Write out the vertex correspondence.
$\Delta ABC \sim \Delta EDF$ means $A\leftrightarrow E$, $B\leftrightarrow D$, $C\leftrightarrow F$, so the true angle equalities are $\angle A=\angle E$, $\angle B=\angle D$, $\angle C=\angle F$.
Step 2: Check each option against this map.
Options (A), (B) and (D) all use side ratios that follow this correspondence correctly, so they are true.
Step 3: Test option (C).
Option (C) claims $\angle A=\angle D$, but the map says $\angle A$ should equal $\angle E$, not $\angle D$, so this statement is false.
\[ \boxed{\text{Option (C)}} \]