Question

if an isosceles triangle △abc is dilated by a scale factor of 3, which of the following statements is not true?
a. △abc is larger than △abc.
b. △abc is similar to △abc.
c. the angles of △abc are congruent to the angles of △abc.
d. the sides of △abc are congruent to the sides of △abc.

Explanation:

Step1: Recall dilation properties

Dilation by a scale - factor \(k = 3>1\) makes the new figure larger. So, \(\triangle A'B'C'\) is larger than \(\triangle ABC\), and option A is true.

Step2: Understand similarity in dilation

Dilation creates similar figures. So, \(\triangle ABC\sim\triangle A'B'C'\), and option B is true.

Step3: Know angle - relationship in dilation

The angles of a figure and its dilated image are congruent. So, the angles of \(\triangle ABC\) are congruent to the angles of \(\triangle A'B'C'\), and option C is true.

Step4: Analyze side - relationship in dilation

When a figure is dilated by a scale factor \(k = 3\), the sides of the new figure are \(k\) times the sides of the original figure. So, the sides of \(\triangle ABC\) are not congruent to the sides of \(\triangle A'B'C'\), and option D is not true.

Answer:

D. The sides of \(\triangle ABC\) are congruent to the sides of \(\triangle A'B'C'\)