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.

Step-by-step 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(1)/(3)\cdot D^(\prime)E^(\prime) \\ EF\cong(1)/(3)\cdot E^(\prime)F^(\prime) \\ DF\cong(1)/(3)\cdot D^(\prime)F^(\prime) \end{gathered}`

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