Question

figure abcd is a dilation of figure abcd about point e with a scale factor of 1.25. li says the figures are neither similar nor congruent. is li correct? use the drop - down menus to explain your answer. click the arrows to choose an answer from each menu. li choose_ correct. each side length of abcd is choose_ the corresponding side length of abcd. each angle measure of abcd is choose_ the corresponding angle measure of abcd. therefore, abcd and abcd are choose_ similar but not congruent similar and congruent neither similar nor congruent

Explanation:

Step1: Recall dilation properties

A dilation with a scale - factor \(k
eq1\) changes the side - lengths of a figure. If the scale factor \(k = 1.25
eq1\), the side - lengths of the dilated figure \(A'B'C'D'\) are \(1.25\) times the side - lengths of the original figure \(ABCD\).

Step2: Recall angle - measure properties in dilation

In a dilation, the angle measures of the pre - image and the image are equal. That is, each angle measure of \(A'B'C'D'\) is equal to the corresponding angle measure of \(ABCD\).

Step3: Determine similarity and congruence

Two figures are similar if their corresponding angles are equal and the ratios of their corresponding side - lengths are equal. Since the angle measures are equal and the ratio of corresponding side - lengths is \(1.25\), the figures are similar. Two figures are congruent if their corresponding angles are equal and their corresponding side - lengths are equal. Since the scale factor is \(1.25
eq1\), the side - lengths are not equal, so the figures are not congruent.

Answer:

Li is not correct. Each side length of \(A'B'C'D'\) is \(1.25\) times the corresponding side length of \(ABCD\). Each angle measure of \(A'B'C'D'\) is equal to the corresponding angle measure of \(ABCD\). Therefore, \(A'B'C'D'\) and \(ABCD\) are similar but not congruent.