Activities

1. Name the transformations that will preserve congruency.

2. Given triangle ABC, will the resulting image be congruent after a reflection over the x-axis and a rotation of 90° counter-clockwise?

3. Is trapezoid ABCD congruent to trapezoid QRST?  Explain your reasoning.

4. Show and explain how ΔABC is congruent to ΔXYZ using a series of transformations.

5. Create your own congruency problem to give to a partner using the guidelines below.
   
   
   1. Draw a polygon on a coordinate grid.
   2. Apply two transformations that will maintain congruency.
   3. Create a question with the original polygon and the final image after the two transformations and ask your partner to identify the transformations.
   4. Create an answer key showing and describing the original image, missing image, final image and the transformations that were done.

Answer Key/Rubric

1. Reflections, rotations, and translations

2. Yes

3. Yes
   Acceptable reasons may include, but are not limited to:

• After two reflections trapezoid ABCD will land on trapezoid QRST
• Trapezoid ABCD can be reflected over the line y = 2 then reflected over the y-axis
• Trapezoid ABCD can be reflected over the y-axis then reflected over the line y = 2
• Reflections preserve congruency
• Graph:

4. Acceptable answers may include, but are not limited to:

• Reflect ΔABC over the y-axis then translated down 6 units

• Translate ΔABC down 6 units then reflect over the y-axis

5. Student created problems will vary.
   Things to look for include, but are not limited to:

• Original shape is a polygon.
• Two transformations are performed that are reflections, rotations, or translations.
• Transformations are performed and labeled accurately
• Answer key should include the original polygon, the final polygon, and the middle polygon along with the necessary steps and labels