Getting Started 
Misconception/Error The student does not understand congruence in terms of rigid motion. 
Examples of Student Work at this Level The student is unable to explain congruence in terms of rigid motion. Instead, the student explains that congruent figures:
 Have the same shape and same size.
 Have congruent angles and congruent sides.
 Remain congruent when they undergo rigid motions.
 Can be shown to be congruent by making them â€śoverlap.â€ť
The student provides descriptions of translation, rotation, and/or reflection.

Questions Eliciting Thinking What are rigid motions? Can you think of any examples of rigid motion?
Can you define the word congruence in terms of rigid motion?
How might you tell if two figures are congruent? Can you explain this in terms of rigid motion? 
Instructional Implications If needed, review the definition of each of the rigid motions (translations, reflections, and rotations). Provide extensive handson opportunities for the student to experiment with rigid motions and to become familiar with the terminology used to describe them.
Review the definition of congruence in terms of rigid motion. Explain that two figures are congruent if there is a sequence of rigid motions that carries one figure onto the other. Assist the student in applying the definition of congruence in terms of rigid motion to show that two figures are congruent. Provide the student with two congruent figures (e.g., a pair of triangles or a pair of quadrilaterals) that are related by a single rigid motion, and ask the student to identify and describe the specific rigid motion that carries one figure onto the other. Explain to the student that describing the rigid motion in detail (e.g., by specifying the center and degree of rotation, the line of reflection, or the vector along which a figure is translated) and then performing the rigid motion is a convincing way to show that the two figures are congruent. Next provide two congruent figures that are related by more than one rigid motion. Have the student identify and describe the sequence of rigid motions that carries one figure onto the other. Ask the student to perform the sequence of rigid motions to ensure the figures are congruent. Provide assistance as needed. 
Making Progress 
Misconception/Error The studentâ€™s explanation is incomplete. 
Examples of Student Work at this Level The studentâ€™s explanation is missing an important component. For example, the student:
 Explains that two figures are congruent if one can be translated to form the other.
 Explains that two figures are congruent if one can be translated, reflected, or rotated to coincide with the other.
 Does not make clear that the figures must coincide after the rigid motion.

Questions Eliciting Thinking What if one of the figures is carried to the other by a rotation or a reflection? Would the figures be congruent?
What if a combination of rigid motions is needed to carry one figure onto the other? Would the figures be congruent?
Can you just move two figures using rigid motion to show they are congruent? Can you show a triangle is congruent to a rectangle by using rigid motion? 
Instructional Implications Review the definition of congruence in terms of rigid motion. Explain that two figures are congruent if there is a sequence of rigid motions that carries one figure onto the other. Assist the student in revising his or her explanation to encompass other cases.
Provide opportunities to show two figures are congruent by performing and describing a sequence of rigid motions that carry one figure onto the other. Include figures requiring each of the rigid motions and various combinations of them. Remind the student to include all necessary components in each description: the center and degree of rotation, the line of reflection, or the vector along which a figure is translated. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student explains that two figures are congruent if one can be carried onto the other by a sequence of rotations, reflections, and translations. 
Questions Eliciting Thinking If two figures are congruent, what must be true of their corresponding angles? What property of rigid motions ensures this?
If two figures are congruent, what must be true of corresponding sides? What property of rigid motions ensures this?
Are congruent figures necessarily similar? Are similar figures necessarily congruent? 
Instructional Implications Ask the student to use the definition of congruence in terms of rigid motion to show that two given figures are congruent. 