Defining Similarity
| Site: | Saylor Academy |
| Course: | GKT101: General Knowledge for Teachers – Math |
| Book: | Defining Similarity |
| Printed by: | Guest user |
| Date: | Wednesday, May 14, 2025, 8:40 PM |
Description
In this lecture, the transformations you have learned about previously are used to define similar shapes. Watch this video and complete the interactive exercises.
Similar shapes & transformations
Source: Khan Academy, https://www.khanacademy.org/math/geometry-home/similarity
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.
Practice
Similarity & transformations - Questions
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.
Similarity & transformations - Answers
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.