Getting Started 
Misconception/Error The student does not understand the AA Similarity Theorem. 
Examples of Student Work at this Level The student is unable to clearly state the theorem and identify its assumptions and conclusion. The student:
 Describes the theorem as involving the congruence of two angles within one triangle.
 Explains the theorem in terms of figures having the same shape.
 Describes the theorem as involving the congruence of two angles in a pair of triangles with a shared side and does not distinguish between the assumption and the conclusion.
 Does not clearly state the theorem or the assumption.

Questions Eliciting Thinking What is the difference between similarity and congruence? Does the AA Theorem referred to in the task ensure the triangles are similar or congruent?
Do you know what the AA Similarity Theorem says? What does the A stand for?
Do you know what the term “assumption” means? What about conclusion? 
Instructional Implications Review the basic form of a conditional statement (e.g., if p, then q). Explain what is meant by the assumption (e.g., what is assumed to be true or given, p) and the conclusion of a conditional statement (e.g., what results when the conditions are met, q). Illustrate with a simple conditional statement such as, “If an angle is a right angle, then its measure is .” Ask the student to identify both the assumption and the conclusion. Next, introduce conditional statements that are not written in ifthen form such as, “A triangle with a right angle is a right triangle.” Ask the student to rewrite the statement in ifthen form (e.g., if a triangle contains a right angle, then it is a right triangle) and identify the assumption (e.g., a triangle contains a right angle), and conclusion (e.g., the triangle is a right triangle). Provide examples of theorems and ask the student to identify the assumptions and conclusion.
Review the definition of similarity in terms of similarity transformations and explain how the definition can be used to show two triangles are similar. Provide opportunities to the student to show two triangles are similar using the definition. Then clearly state the AA Similarity Theorem and ask the student to identify the assumption and the conclusion. Provide a diagram and ask the student to write the assumption and conclusion with reference to the specific triangles shown. Explain that the AA Similarity Theorem describes a condition that guarantees similarity (e.g., the congruence of two pairs of corresponding angles of the triangles). Clarify that the theorem applies only to a pair of triangles.Next, introduce the student to a proof of the AA Similarity Theorem. Then consider implementing the MFAS tasks Justifying a Proof of the AA Similarity Theorem and Prove the AA Similarity Theorem (GSRT.1.3). 
Making Progress 
Misconception/Error The student is unable to provide a definition of similarity in terms of similarity transformations. 
Examples of Student Work at this Level The student identifies both the assumptions (e.g., two pairs of angles of two triangles are congruent) and the conclusion (e.g., the triangles are similar) and draws an appropriate diagram to illustrate the assumptions. However, the student is unable to define similarity in terms of similarity transformations. The student says two triangles are similar if:
 They have the same shape.
 Corresponding angles are congruent and corresponding sides are proportional.
 Two angles of one are congruent to two angles of the other.

Questions Eliciting Thinking Do you know what is meant by a similarity transformation?
What does it mean for two triangles to be similar using the definition of similarity in terms of rigid motions and dilations? 
Instructional Implications Ensure that the student uses appropriate terminology and notation to describe the assumptions and conclusion. Then review the definition of similarity in terms of similarity transformations.Explain how the definition can be used to show two triangles are similar. Provide opportunities for the student to show two triangles are similar using the definition.
Next, introduce the student to a proof of the AA Similarity Theorem. Then consider implementing the MFAS tasks Justifying a Proof of the AA Similarity Theorem and Prove the AA Similarity Theorem (GSRT.1.3). 
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 identifies both the assumptions (e.g., two pairs of angles of two triangles are congruent) and the conclusion (e.g., the triangles are similar) and draws an appropriate diagram to illustrate the assumptions. The student explains that if a triangle can be transformed into another triangle by a sequence of rigid motions and a dilation, then the two triangles are similar. 
Questions Eliciting Thinking What is the advantage to using the AA Similarity Theorem? 
Instructional Implications Ask the student to develop a proof of the AA Similarity Theorem.
Consider implementing the MFAS tasks Justifying a Proof of the AA Similarity Theorem and Prove the AA Similarity Theorem (GSRT.1.3). 