Lesson objective: Determine what happens to parallel sides when a figure undergoes a rigid transformation.

Students bring prior knowledge of parallel lines from 4.G.A.1, and transformations from 8.G.A.1.a. This prior knowledge is extended to bridge a relationship between parallel lines and rigid transformations as students investigate how parallel lines are affected when a figure undergoes a rotation, reflection, or translation. A conceptual challenge students may encounter is coming up with ways to prove that lines are parallel, without just saying that they are because they never cross.

The concept is developed through work with three sets of shapes, which allows students to investigate several scenarios in order to find a big idea.

This work helps students deepen their understanding of equivalence because it is continuing to add on to the definition of what it means to be congruent, and about all the components of shapes that remain equal after a transformation.

Students engage in Mathematical Practice 3 (Construct viable arguments and critique the reasoning of others) as they analyze two students' opinions and then work to prove which one is correct.

**Key vocabulary:**

- congruent
- parallel
- rotation
- transformation

**Special materials needed:**