Question

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

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

Hint:

In similarity notation \(\triangle XYZ \sim \triangle PQR\), position 1 matches position 1 (\(X \leftrightarrow P\)), position 2 matches position 2 (\(Y \leftrightarrow Q\)), and so on. Use this to write ratios correctly every time.

Answer 1

The Correct Option is C

To determine which statement is not true regarding the given similar triangles \(\triangle ABC\) and \(\triangle EDF\), let's analyze each option:

1. \(\frac{\text{Perimeter of } \triangle ABC}{\text{Perimeter of } \triangle EDF} = \frac{AB}{ED}\)
   

   In similar triangles, the ratio of their perimeters is equal to the ratio of their corresponding sides. Therefore, this statement is true.

2. \(\frac{AB}{ED} = \frac{AC}{EF}\)
   

   This is a property of similar triangles, where corresponding sides are proportional. Hence, this statement is true.

3. \(\angle A = \angle D, \angle C = \angle F\)
   

   In similar triangles, all corresponding angles are equal. Therefore, \(\angle A = \angle D\) is true, but \(\angle C = \angle F\) is not directly stated in the question's similarity condition. This suggests the statement might be misleading.

4. \(\frac{AB + BC}{AC} = \frac{ED + DF}{EF}\)
   

   This involves a combination of non-corresponding sides and does not hold true under the properties of similar triangles. This is typically not a true proportionality condition in similar triangles.

After assessing all statements, the option \(\angle A = \angle D, \angle C = \angle F\) stands out as potentially misleading because the equality of angles \(\angle C\) and \(\angle F\) would not impact the similarity since angle \(\angle B\) and \(\angle E\) are the corresponding angles. Furthermore, it is most likely incorrectly narrowing the overall property of equal corresponding angles. Therefore, the correct answer is:

\(\angle A = \angle D, \angle C = \angle F\)