IM G Unit 2 Lesson 3
If triangle [i]ABC[/i] is congruent to triangle [i]A'B'C'[/i]. . .[list=1][*]What must be true?[/*][*]What could possibly be true?[/*][*]What definitely can’t be true?[/*][/list]
Noah and Priya were playing Invisible Triangles. For card 3, Priya told Noah that in triangles [i]ABC[/i] and [i]DEF[/i]:[br][br][i][br][/i]
Here are the steps Noah had to tell Priya to do before all 3 vertices coincided:[br][list][*]Translate triangle [i]ABC[/i] by the directed line segment from [i]A[/i] to [i]D[/i].[/*][*]Rotate the image, triangle [i]A'B'C'[/i], using [i]D[/i] as the center, so that rays [i]A"B"[/i] and [i]DE[/i] line up.[/*][*]Reflect the image, triangle [i]A"B"C"[/i], across line [i]DE[/i].[/*][/list]
After those steps, the triangles were lined up perfectly. Now Noah and Priya are working on explaining why their steps worked, and they need some help. Answer their questions.
[list=1][*]We know that rays [i]A"B"[/i] and [i]DE [/i]line up because we said they had to, but why do points [i]B"[/i] and [i]E[/i] have to be in the exact same place?[/*][/list]
After the reflection of triangle [i]A"B"C"[/i] across [i]DE.[/i][list=1][*]How do we know that now, the image of ray and ray will line up?[/*][*]How do we know that the image of point and point will line up exactly?[/*][/list]
IM G Unit 2 Lesson 3 from IM Geometry by Illustrative Mathematics, [url=https://im.kendallhunt.com/HS/students/2/2/1/index.html]https://im.kendallhunt.com/HS/students/2/2/3/index.html[/url]. Licensed under the Creative Commons Attribution 4.0 license, [url=https://creativecommons.org/licenses/by/4.0/]https://creativecommons.org/licenses/by/4.0/[/url].