Getting Started 
Misconception/Error The student’s proof shows no evidence of an overall strategy or logical flow. 
Examples of Student Work at this Level The student does not use triangle congruence or properties of a parallelogram in the proof. The student:
 Draws diagonal but then assumes, rather than proves, that and are bisected by diagonal .
 Makes some observations about the rhombus without regard to the statement to be proven.
 Determines that and are bisected by diagonal by “definition of an angle bisector.”
 Uses the statement to be proven as a justification in its own proof.

Questions Eliciting Thinking What is it that you are given and what are you trying to prove?
Is diagonal shown in the diagram? Did you think to draw it? If you draw it, what two geometric figures are formed? How can these figures assist you with the planning of your proof?
What properties of parallelograms or rhombuses might help you with this proof?
What markings are used to indicate congruent parts on a diagram? Can you mark the diagram to show congruent parts? How can these congruent parts help you design a plan for this proof?
Did you think of a plan for your proof before you started? 
Instructional Implications Review the properties of a rhombus. Ask the student to draw diagonal and to consider what can be concluded if the two triangles formed are congruent. Assist the student in devising an overall strategy for the proof: (1) Draw the diagonal to form two triangles. (2) Show the two triangles are congruent. (3) Use the congruence to conclude that = and = and complete the proof. Guide the student through the statements of the proof and prompt the student to supply the justifications.
Emphasize that a theorem cannot be used as a justification in its own proof. Encourage the student to first determine what is available to use in a proof of a particular statement.
If needed, review the ways to prove two triangles congruent (SSS, SAS, ASA, AAS, HL) and what must be established in order to conclude two triangles are congruent when using each method. Remind the student that once two triangles are proven congruent, all remaining pairs of corresponding parts can be shown to be congruent.
Encourage the student to begin the proof process by developing an overall strategy. Provide another statement to be proven and have the student compare strategies with another student and collaborate on completing the proof.
Provide additional opportunities to construct proofs of statements involving congruent or similar triangles. 
Moving Forward 
Misconception/Error The student’s proof shows some evidence of an overall strategy but fails to establish major conditions and/or includes incorrect statements. 
Examples of Student Work at this Level The student is unable to show that but can use this fact to complete the proof.

Questions Eliciting Thinking What is your general strategy for this proof?
How can you show the two triangles are congruent?
What do you need to show in order to use the SAS (or SSS) congruence theorem? Have you done this in your proof?
Have you included statements that are unnecessary? 
Instructional Implications Review the ways to prove two triangles congruent (SSS, SAS, ASA, AAS, HL) and what must be established in order to conclude two triangles are congruent when using each method. Provide more opportunities and experiences with proving triangles congruent.
Review an overall strategy for the proof and guide the student through the steps of any part of his or her proof that was incomplete. Prompt the student to provide justifications for each step.
Provide additional opportunities to construct proofs of statements involving congruent or similar triangles. 
Almost There 
Misconception/Error The student’s proof contains a minor error. 
Examples of Student Work at this Level The student:
 Makes an error in a statement or justification.
 Includes unnecessary statements such as .
 Uses notation or names angles incorrectly.

Questions Eliciting Thinking There is an error in this statement. Can you compare it to the diagram and find the error?
Did you use the fact that in your proof?
How is the notation for the name of a side different from the notation for the length of a side? How is the notation for the name of an angle different from the notation for the measure of an angle?
There are three different angles with point A as a vertex. What did you mean by ? 
Instructional Implications Provide the student with feedback on his or her proof. If the student omitted a statement, have the student go through each step of the proof to see if he or she can find the gap in the logical flow of the proof. If the student included an unnecessary statement, challenge the student to find the statement and remove it. Prompt the student to supply justifications or statements that are missing. If necessary, review notation for naming sides, lengths of sides, angles, and angle measures. Also, review that when naming congruent triangles, vertices are named in corresponding order.
Provide additional opportunities to construct proofs of statements involving congruent or similar triangles. 
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 uses the SSS Congruence Theorem or the SAS Congruence Theorem to show that and concludes that and as a consequence of the congruence. The student then concludes that both and are bisected by diagonal .

Questions Eliciting Thinking Can you think of another way to prove this statement?
Is this statement also true of diagonal ?
Is this statement generally true of parallelograms? Why or why not? 
Instructional Implications Challenge the student to determine which of the following statements are true:
 The diagonals of a rectangle are congruent.
 The diagonals of a parallelogram each bisect a pair of opposite angles.
 Opposite angles of a kite are congruent.
 The diagonals of a square are perpendicular.
Then ask the student to write a proof of the statements that are true. 