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... .

Explanation:

Step1: Properties of Dilation

Dilation is a transformation that changes the size of a figure but not its shape. If the scale factor \(k = 1.25
eq1\), the side - lengths of the dilated figure \(A'B'C'D'\) and the original figure \(ABCD\) are related by \(s_{A'B'C'D'}=k\times s_{ABCD}\). So, each side length of \(A'B'C'D'\) is \(1.25\) times the corresponding side length of \(ABCD\).

Step2: Angle - measure in Dilation

Angles are preserved in a dilation. That is, for any angle \(\angle X\) in \(ABCD\) and its corresponding angle \(\angle X'\) in \(A'B'C'D'\), \(\angle X=\angle X'\).

Step3: Similarity and Congruence

Two figures are congruent if their corresponding side - lengths and angle - measures are equal (scale factor \(k = 1\)). Two figures are similar if their corresponding angles are equal and the ratios of their corresponding side - lengths are equal (here the ratio of side - lengths is the scale factor \(k = 1.25\)). Since the scale factor \(k=1.25
eq1\), the figures are not congruent, but they are similar.

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.