Defining Similarity

1. In conclusion, a rectangle is sometimes similar to another rectangle, because we can sometimes map one onto the other using only dilations and rigid transformations.

2. Erin concluded:

"I was able to map line segment \(\overline{A B}\) onto line segment \(\overline{C B}\) using a sequence of rigid transformations and dilations, so the figures are similar".

There is no error. This is a correct conclusion.

3. Sabrina concluded:

"I was able to map circle \(P\) onto circle \(R\) using a sequence of rigid transformations and a dilation, so the figures are similar".

There is no error. This is a correct conclusion.

4. Konnor concluded:

"The quadrilaterals have four pairs of congruent corresponding angles, so the figures are similar".

It's impossible to map \(S T U V\) onto \(W X Y Z\) using only rigid transformations and dilations, so the figures are not similar.