Question

are quadrilaterals abcd and efgh similar?
yes, quadrilaterals abcd and efgh are similar because a translation of (x + 2, y + 5) and a dilation by the scale - factor of 3 from point a map quadrilateral abcd onto efgh.
no, quadrilaterals abcd and efgh are not similar because their corresponding segments are not proportional.
yes, quadrilaterals abcd and efgh are similar because a translation of (x, y + 3) and a dilation by the scale - factor of 3 from point d map quadrilateral abcd onto efgh.
no, quadrilaterals abcd and efgh are not similar because their corresponding angles are not congruent.

Explanation:

Step1: Recall similarity criteria

Two polygons are similar if there is a sequence of rigid - motions (translations, rotations, reflections) and dilations that map one polygon onto the other. This implies that corresponding angles are congruent and corresponding sides are proportional.

Step2: Analyze given transformations

If a translation of \((x + 2,y + 5)\) and a dilation by a scale factor of 3 from a point map quadrilateral \(ABCD\) onto \(EFGH\), then the corresponding angles of \(ABCD\) and \(EFGH\) are congruent (because translations and dilations preserve angle - measure) and the corresponding sides of \(ABCD\) and \(EFGH\) are proportional (since dilation multiplies the lengths of the sides by a constant scale factor).

Answer:

Yes, quadrilaterals \(ABCD\) and \(EFGH\) are similar because a translation of \((x + 2,y + 5)\) and a dilation by the scale factor of 3 from point \(A'\) map quadrilateral \(ABCD\) onto \(EFGH\)