MAFS.912.G-SRT.1.3

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: Level 2: Basic Application of Skills & Concepts
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
Date of Last Rating: 02/14
Status: State Board Approved
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

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912070: Access Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022 (current), 2022 and beyond)
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
7912065: Access Geometry (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-SRT.1.AP.3a: Apply the angle-angle (AA) criteria for triangle similarity on two triangles.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 4 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Formative Assessments

Justifying a Proof of the AA Similarity Theorem:

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

Type: Formative Assessment

Prove the AA Similarity Theorem:

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

Type: Formative Assessment

Describe the AA Similarity Theorem:

Students are asked to describe the AA Similarity Theorem.

Type: Formative Assessment

Lesson Plans

How Much Proof Do We Need?:

In this lesson plan, students determine the minimum amount of information needed to prove if two triangles are similar.

Type: Lesson Plan

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.

Type: Lesson Plan

MFAS Formative Assessments

Describe the AA Similarity Theorem:

Students are asked to describe the AA Similarity Theorem.

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.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.