# im.g.1.10.3.Does Order Matter?

Two figures are called CONGRUENT if a sequence of rigid transformations takes one figure onto another.
In this activity we explore the steps of a sequence (or sequences) that will map the pre-image onto its image. We will also look at whether the order of those steps matters. Specifically, will reversing the steps also work?

1. Describe a sequence of transformations that will take figure A onto figure B. (We could also say: "Construct a composition that maps preimage A onto image B.") [You can use the GeoGebra tools with this applet to verify whether or not your steps work.]

2. If you reverse the order of your sequence, will the reverse sequence still take A onto B?

3. Describe a sequence of transformations that will take figure A onto figure C. (You may try doing your sequence to verify it works using the tools in the applet).

4. If you reverse the order of your sequence, will the reverse sequence still take A onto C? Explain.

## Attribution:

illustrative mathematics. geometry. unit 1. section 10. activity 3. "Does order matter?"
https://im.kendallhunt.com/HS/teachers/2/1/10/index.html
Licensed under the Creative Commons Attribution 4.0 license
https://creativecommons.org/licenses/by/4.0/