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 sequence of rigid motions that does not map one triangle onto the other.
 Is too vague when describing whether or not the sequence of rigid motions maps ABC onto DEC.
 Writes that because all of the sides and the angles are congruent, the triangles are congruent.
 Describes reflecting ABC over point C rather than over a line containing point C.

Questions Eliciting Thinking Can you explain in more detail how this sequence of rigid motions will map ABC onto DEC?
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 ABC onto DEC?
What does it mean to reflect a figure over a point rather than a line? 
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 ABC on patty paper or a transparency. Ask the student to use the transparency to model a sequence of rigid motions that maps ABC onto DEC 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. Clear up any further misconceptions the student may have about point versus line symmetry. 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 ABC onto DEC. 
Examples of Student Work at this Level The student:
 Describes a reflection over a line drawn between points B and E and through point C but includes no other stipulations for the line.
 Does not include in the description the center of rotation or justify the conclusion that a reflection results in sides or vertices coinciding.

Questions Eliciting Thinking Specifically, where does the line of reflection need to lie between point B and point E? How do you know that point A will lie on top of point D after the reflection?
What happened after the reflection? Did any sides 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? 
Instructional Implications Explain to the student the need for a specific description for the location of the line of reflection. Demonstrate using graph paper or interactive software how moving the line of reflection alters the location of the reflected image. 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 ABC onto DEC and concludes that:
 A pair of corresponding vertices such as B and E coincide without appealing to the assumption that .
 A pair of lines that contain sides will coincide such as and without appealing to the assumption .

Questions Eliciting Thinking How do you know that vertices B and E will coincide?
How do you know that and will align? 
Instructional Implications Show the student any statement that requires justification and ask the student to provide one. 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. Remind 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:
 Rotate ABC clockwise around point C until aligns with (the degree of rotation is equal to the measure of ). Since , point B coincides with point E.
 Reflect ABC across (or ). Since and aligns with , then aligns with . Since , point A coincides with point D.
 Since the vertices of ABC coincide with the vertices of DEC, ABC DEC.

Questions Eliciting Thinking How can you describe the degree of your rotation?
Did you need to use all of the given information (all sides and angles congruent) to show that ABC DEC? 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). 