IM Geo.2.3 Lesson: Congruent Triangles, Part 1
If triangle ABC is congruent to triangle A'B'C'...
What must be true?
What could possibly be true?
What definitely can’t be true?
Player 2 use the applet to sketch the transformations while Player 1 is giving instructions.
Replay invisible triangles, but with a twist. This time, the transformer can only use reflections—the last 2 sentence frames on the transformer card. You may wish to include an additional sentence frame: Reflect _____ across the angle bisector of angle _____.
Noah and Priya were playing Invisible Triangles. For card 3, Priya told Noah that in triangles ABC and DEF:
Here are the steps Noah had to tell Priya to do before all 3 vertices coincided:
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.
First, we translate triangle by the directed line segment from to . Point will coincide with because we defined our transformation that way. Then, rotate the image, triangle , by the angle , so that rays and line up.
We know that rays and line up because we said they had to, but why do points and have to be in the exact same place?
Finally, reflect the image, triangle A''B''C'' across DE.
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?