Getting Started 
Misconception/Error The student describes a sequence of rigid motions that does not map one triangle onto the other. 
Examples of Student Work at this Level The student:
 Describes a reflection, translation, and rotation that do not map onto .
 Is too vague when describing whether or not the sequence of rigid motions maps onto .
 Indicates he or she cannot perform a rotation without the origin.

Questions Eliciting Thinking Can you explain in more detail how this sequence of rigid motions will map onto ?
How could you use rigid motion to move one triangle directly on top of the other? Can you identify a rigid motion or sequence of rigid motions that will map onto ?
How could you describe a rotation without using the origin? Are there other points that you could use as the center of the rotation? 
Instructional Implications Review the definition of each of the rigid motions: translations, reflections, and rotations. To develop an intuitive understanding of rigid transformations, allow the student to experiment with a variety of transformations using transparent paper or interactive websites. Be sure the student understands not only how to perform a rigid motion but how to describe it using correct terminology and notation.
Have the student trace on patty paper or a transparency. Ask the student to use the transparency to model a sequence of rigid motions that maps onto providing assistance as needed. Allow the student to experiment with a variety of rigid motions. Once the student has successfully identified a sequence of rigid motions, assist the student in describing the sequence using correct terminology and notation. Provide the student with several other examples of congruent triangles and have the student first model the rigid motions that map one triangle onto the other and then describe them. 
Moving Forward 
Misconception/Error The student does not completely describe the sequence of rigid motions that maps onto . 
Examples of Student Work at this Level The student:
 Does not include in the description the vector along which the figure is translated and/or the center and degree of rotation.
 Does not include the mapping of a vertex or side of one triangle onto the other.

Questions Eliciting Thinking Can you describe in more detail how this sequence of rigid motions will map one triangle onto the other?
What vector could you identify that describes how the figure was translated? What happened after the translation? Did any of the vertices coincide?
Is it possible to identify both the center and the degree of rotation? What is the direction of rotation? What happened after the rotation? Did any of the sides coincide?
How do you know point C coincides with point F? 
Instructional Implications Model for the student a clear and complete explanation of the student’s sequence of rigid motions. Provide the student with several other examples of congruent triangles and have the student identify the sequence of rigid motions that maps one triangle onto the other. Remind the student to be as clear and concise as possible in the description, identifying specifically the center and degree of rotation, the line of reflection, or the vector along which a figure is translated. If possible, have the student ask another student to read his or her description to see if it can be followed without further explanation.
Explain to the student that two triangles can be shown congruent by describing a sequence of rigid motions that results in corresponding vertices coinciding. Consequently, it is important to explicitly state when vertices or sides are mapped onto corresponding vertices or sides by a transformation and to provide a justification for these occurrences. Prompt the student to be mindful of any assumptions made (the “given”) and to determine if the assumptions were used in the proof. 
Almost There 
Misconception/Error The student does not adequately justify some statements in the proof. 
Examples of Student Work at this Level The student correctly describes a sequence of rigid motions that maps onto and concludes that:
 A pair of corresponding vertices such as C and F coincide without appealing to the assumption that .
 A pair of lines that contain sides will coincide such as and without appealing to the assumption that .

Questions Eliciting Thinking How do you know that vertices C and F will coincide?
How do you know that and will align? 
Instructional Implications Show the student any statements that require justification and ask the student to provide them. Explain to the student that two triangles can be shown congruent by describing a sequence of rigid motions that results in corresponding vertices coinciding. Consequently, it is important to explicitly state when vertices or sides are mapped onto corresponding vertices or sides by a transformation and to provide a justification for these occurrences. Prompt the student to be mindful of any assumptions made (the “given”) and to determine if the assumptions were used in the proof. 
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 reasons as follows:
 Translate along (seven units to the right and three units up) so that point A coincides with point D.
 Rotate 45° clockwise about point D so that aligns with . Since , point C now coincides with point F.
 Since , point A coincides with point D, and aligns with then aligns with . Since , point B now coincides with point E.
 Since the vertices coincide with the vertices of , .

Questions Eliciting Thinking Did you need to use all of the given information (all sides and angles congruent) to show that ? If not, what information was not necessary? 
Instructional Implications Discuss the SSS, SAS, and ASA congruence theorems with the student. Ask the student which of these is implied in his or her explanation.
Consider implementing one of the following MFAS tasks: Justifying Side Angle Side Congruence (GCO.2.8), Justifying Angle Side Angle Congruence (GCO.2.8), Justifying Side Side Side Congruence (GCO.2.8). 