Defining Similarity

1. Complete the similarity statement.

A rectangle is ________ (sometimes/always/never) similar to another rectangle, because we can ________ (sometimes/always/never) transformations.

2. Erin was able to map line segment $\overline{A B}$ onto line segment $\overline{C B}$ using a rotation and a dilation.

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".

What error did Erin make in her conclusion?

(A) Erin used a dilation, so the segments aren't similar.

(B) The segments are congruent, not similar.

(C) There is no error. This is a correct conclusion.

3. Sabrina was able to map circle $P$ onto circle $R$ (with $Q$ and $S$ being on each circle, respectively) using a translation and a dilation.

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".

What error did Sabrina make in her conclusion?

Choose 1 answer:

(A) Sabrina used a translation, so the circles aren't similar.

(B) Sabrina used a dilation, so the circles aren't similar.

(C) There is no error. This is a correct conclusion.

4. Konnor was curious if quadrilaterals $S T U V$ and $W X Y Z$ were similar, so he considered their angles.

Konnor concluded:

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

What error did Konnor make in his conclusion?

Choose 1 answer:

(A) The quadrilaterals are congruent, not similar.

(B) 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.

(C) There is no error. This is a correct conclusion.

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.