Question

triangle DEF was dilated by a scale factor of 3 to create triangle D^ prime EF Which of the following statements is true?

Answer 1

Given:

A triangle ∆DEF is dilated to ∆D'E'F'.

The scale factor of a dilation is 3.

The objective is to choose the correct answers.

Explanation:

Considering the angles of the triangle, the dilation of any triangle will never change the angles of the triangle.

$\begin{gathered} \angle D=\angle D^{\prime} \\ \angle E=\angle E^{\prime} \\ \angle F=\angle F^{\prime} \end{gathered}$

Considering the sides of the triangle, the relation between the sides of the triangle ∆DEF and ∆D'E'F' can be written as,

$\begin{gathered} DE\cong\frac{1}{3}\cdot D^{\prime}E^{\prime} \\ EF\cong\frac{1}{3}\cdot E^{\prime}F^{\prime} \\ DF\cong\frac{1}{3}\cdot D^{\prime}F^{\prime} \end{gathered}$

Hence, options (2) and (4) are the correct answer.