EDSS 4501M Congruent Triangles and Rigid Motions

Author:
Vanessa

Given ABC, find the series of rigid motions that maps it onto DEF. You can use vector u to model translations. Write the rigid motions your group used here. Make sure to be specific with any units of translation, lines of reflection, and/or degrees of rotation.

How do you know ABC is congruent to DEF?

Now that you have identified one series of rigid motions that mapped ABC onto DEF, come up with a different series of rigid motions that proves these two triangles are congruent. Write down the other set of rigid motions you used here. Make sure to be specific with any units of translation, lines of reflection, and/or degrees of rotation.

Below we have some triangles and tools given that will help you create your own mappings. Some things to note: - ABC (in pink) is the original triangle, you may change the points on this triangle in any way that you want. **Make sure to start with this one!** - Segment XY can be moved in any way. It reflects ABC onto DEF. -Vector u translates DEF. - Point P is the point of rotation that rotates ABC into GHI. It can be moved anywhere. Use the slider α to control the rotation. -Vector v translates GHI. - Segment ZW can be moved in any way. It reflects GHI onto JKL. Create your own mapping using these rigid motions to prove that two of any of these triangles are congruent. Use at least two rigid motions.

Write down the series of rigid motions your group used to map one triangle onto another. Make sure to be specific with any units of translation, lines of reflection, and/or degrees of rotation. Write congruence statements for your two triangles.