Standard #: MAFS.912.G-SRT.1.3 (Archived Standard)


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Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.


General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Similarity, Right Triangles, & Trigonometry
Cluster: Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 2: Basic Application of Skills & Concepts - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    Also assesses:

    MAFS.912.G-SRT.2.4

    Assessment Limits :
    Items may require the student to be familiar with using the algebraic
    description begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis x plus a comma y plus b right parenthesis end style for a translation, and
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis k x comma k y right parenthesis end style for a dilation when given the center of dilation.
    Items may require the student to be familiar with the algebraic
    description for a 90-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis negative y comma x right parenthesis end style, for a 180-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis negative x comma negative y right parenthesis end style , and for a 270-degree rotation about the origin,
    begin mathsize 12px style left parenthesis x comma y right parenthesis rightwards arrow left parenthesis y comma negative x right parenthesis end style . Items that use more than one transformation may
    ask the student to write a series of algebraic descriptions.
    Calculator :

    Neutral

    Clarification :
    Students will explain using properties of similarity transformations
    why the AA criterion is sufficient to show that two triangles are
    similar.

    Students will use triangle similarity to prove theorems about
    triangles.

    Students will prove the Pythagorean theorem using similarity. 

    Stimulus Attributes :
    Items may be set in a real-world or mathematical context.
    Response Attributes :

    None



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Related Resources

Formative Assessments

Name Description
Justifying a Proof of the AA Similarity Theorem

Students are asked to justify statements of a proof of the AA Similarity Theorem.

Prove the AA Similarity Theorem

Students will indicate a complete proof of the AA Theorem for triangle similarity.

Describe the AA Similarity Theorem

Students are asked to describe the AA Similarity Theorem.

Lesson Plans

Name Description
How Much Proof Do We Need?

Students determine the minimum amount of information needed to prove that two triangles are similar.

Geometry Problems: Circles and Triangles

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

  • Solving problems by determining the lengths of the sides in right triangles.
  • Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

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