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: Recall dilation properties

A dilation is a transformation that changes the size of a figure, but not its shape. The scale - factor is 1.25, so the side - lengths of the dilated figure \(A'B'C'D'\) are related to the side - lengths of the original figure \(ABCD\).

Step2: Analyze side - length relationship

If the scale factor is \(k = 1.25\), then each side length of \(A'B'C'D'\) is \(1.25\) times the corresponding side length of \(ABCD\).

Step3: Analyze angle - measure relationship

The angle measures of a figure are preserved under dilation. So each angle measure of \(A'B'C'D'\) is equal to the corresponding angle measure of \(ABCD\).

Step4: Determine similarity and congruence

Since the corresponding angles are equal and the corresponding sides are in proportion (with a scale factor of 1.25), the two figures are similar. They are not congruent because the side - lengths are not equal (scale factor \(
eq1\)). So Li is incorrect.

Answer:

Li is incorrect. 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.