Question

question 3 (multiple choice worth 1 points) (03.02r mc) are quadrilaterals abcd and efgh similar? yes, quadrilaterals abcd and efgh are similar because a translation of (x + 2, y + 4) and a dilation by the scale factor of 2 from point d map quadrilateral abcd onto efgh yes, quadrilaterals abcd and efgh are similar because a translation of (x + 3, y + 4) and a dilation by the scale factor of 2 from point a map quadrilateral abcd onto efgh no, quadrilaterals abcd and efgh are not similar because their corresponding angles are not congruent no, quadrilaterals abcd and efgh are not similar because their corresponding segments are not proportional

Explanation:

Step1: Check similarity conditions

Similarity requires corresponding angles congruent and corresponding sides proportional.

Step2: Analyze side lengths

Let's assume side lengths. For example, if \(AB = 1\) unit (counting grid - squares), \(HE=2\) units.

Step3: Check transformation

A translation \((x + 3,y + 4)\) (if we assume coordinate - like movement from \(ABCD\) to \(EFGH\)) and a dilation by scale factor \(2\) (since side lengths of \(EFGH\) are double of \(ABCD\)) from a non - relevant point (not \(A\) as \(A\) to \(H\) is not the center of dilation in terms of the figure's relation) does not map \(ABCD\) to \(EFGH\) correctly. Also, angles: Since the shapes are parallelograms (by grid - based side - parallelism), but the side - length ratio is not maintained in a way that would come from a proper similarity transformation (with a single center of dilation). The corresponding angles of parallelograms \(ABCD\) and \(EFGH\) are congruent (opposite angles of parallelograms are equal and adjacent angles are supplementary in both), but the corresponding segments (sides) are not proportional. For example, if \(AB\) is considered as a side, \(HE\) (a corresponding - looking side) is not in proportion with other sides when considering a single scale factor for the whole quadrilateral.

Answer:

No, quadrilaterals \(ABCD\) and \(EFGH\) are not similar because their corresponding segments are not proportional.