Download Describe the AA Similarity Theorem

Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 72987
Describe the AA Similarity Theorem
Students are asked to describe the AA Similarity Theorem.
Subject(s): Mathematics
Grade Level(s): 9, 10, 11, 12
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, similar, triangle, AA theorem
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DescribeTheAASimilarityTheorem_Worksheet.docx
MFAS_DescribeTheAASimilarityTheorem_Worksheet.pdf
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Describe the AA Similarity Theorem worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
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.
page 1 of 3 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 (G-SRT.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
page 2 of 3 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 (G-SRT.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 (G-SRT.1.3).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Describe the AA Similarity Theorem worksheet
SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.912.G-SRT.1.3:
Description
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
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