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IM G Unit 2 Lesson 3

Autor:Mrs.Kliewer, IM Algebra 1, Geometry, Algebra 2

 If triangle ABC is congruent to triangle A'B'C'. . .

  1. What must be true?
  2. What could possibly be true?
  3. What definitely can’t be true?

Noah and Priya were playing Invisible Triangles. For card 3, Priya told Noah that in triangles ABC and DEF:
Image
Here are the steps Noah had to tell Priya to do before all 3 vertices coincided:
  • Translate triangle ABC by the directed line segment from A to D.
  • Rotate the image, triangle A'B'C', using D as the center, so that rays A"B" and DE line up.
  • Reflect the image, triangle A"B"C", across line DE.
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.

  1. We know that rays A"B" and  DE line up because we said they had to, but why do points B" and E have to be in the exact same place?

After the reflection of triangle A"B"C" across DE.

  1. How do we know that now, the image of ray  and ray  will line up?
  2. How do we know that the image of point  and point  will line up exactly?

IM G Unit 2 Lesson 3 from IM Geometry by Illustrative Mathematics, https://im.kendallhunt.com/HS/students/2/2/3/index.html. Licensed under the Creative Commons Attribution 4.0 license, https://creativecommons.org/licenses/by/4.0/.

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