Question

δabc was dilated from the origin by a scale factor to create δabc. which of the following is true for the similar triangles? side ac is proportional to side ca. side ac is proportional to side ab. side ac is proportional to side ac. side ac is proportional to side ab.

Explanation:

Step1: Recall dilation property

When a triangle is dilated, corresponding sides of the original and dilated triangles are proportional.
In \(\triangle ABC\) and \(\triangle A'B'C'\), side \(AC\) in \(\triangle ABC\) corresponds to side \(A'C'\) in \(\triangle A'B'C'\).

Step2: Analyze options

Option 1: Side \(AC\) and side \(CA\) are the same side in \(\triangle ABC\), not a proportional - relationship in the context of dilation.
Option 2: Side \(AC\) and side \(AB\) are sides of the same triangle \(\triangle ABC\), not related by dilation.
Option 3: Since \(AC\) and \(A'C'\) are corresponding sides of the dilated triangles \(\triangle ABC\) and \(\triangle A'B'C'\), they are proportional.
Option 4: Side \(AC\) and side \(A'B'\) are not corresponding sides of the dilated triangles.

Answer:

Side AC is proportional to side A'C'.