MAFS.912.G-SRT.1.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
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

  • 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 use the definition of similarity in terms of similarity
    transformations to decide if two figures are similar.

    Students will explain using the definition of similarity in terms of
    similarity transformations that corresponding angles of two figures
    are congruent and that corresponding sides of two figures are
    proportional.

  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context
  • Response Attributes :
    Items may ask the student to determine if given information is
    sufficient to determine similarity.
Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question:

    Triangle RTV is shown on the graph.

    Triangle R'T'V' is formed using the transformation (0.2x, 0.2y) centered at (0,0).

    Select the three equations that show the correct relationship between the two triangles based on the transformation.

     

     

  • Difficulty: N/A
  • Type: MS: Multiselect

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.2a: Determine if two figures are similar.
MAFS.912.G-SRT.1.AP.2b: Given two figures, determine whether they are similar and explain their similarity based on the equality of corresponding angles and the proportionality of corresponding sides.

Related Resources

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

Assessments

Sample 3 - High School Geometry State Interim Assessment:

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

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

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

Type: Assessment

Formative Assessments

Showing Similarity:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar.

Type: Formative Assessment

The Consequences of Similarity:

Students are given the definition of similarity in terms of similarity transformations and are asked to explain how this definition ensures the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

Type: Formative Assessment

To Be or Not To Be Similar:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar.

Type: Formative Assessment

Lesson Plans

Coding Geometry Challenge #23 & 24:

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Transformation and Similarity:

Using non-rigid motion, students determine that two polygons are similar.

Type: Lesson Plan

Congruence vs. Similarity:

Students will learn the difference between congruence and similarity of classes of figures (such as circles, parallelograms) in terms of the number of variable lengths in the class. A third category will allow not only rigid motions and dilations, but also a single one-dimensional stretch, allowing more classes of figures to share sufficient common features to belong.

Type: Lesson Plan

Dilation Transformation:

  • This lesson is designed to instruct students to identify dilations, verify that two polygons are similar, and use the dilation rule to map dilations.
  • There are task cards (with and without QR codes) provided for independent practice. The students will need to download a free QR code reader app onto their smartphones if you choose to use the cards with QR codes.

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

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 and 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

Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

The Chaos Machine:

The "machine" generates 5000 points based upon a random selection of points. Each point is chosen iteratively to be a particular fraction of the way from a current point to a randomly chosen vertex. For carefully chose fractions, the results are intriguing fractal patterns, belying the intuition that randomness must produce random-looking outputs.

Type: Problem-Solving Task

Are They Similar?:

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

Type: Problem-Solving Task

Text Resource

Fractal Geometry Overview:

This informational text resource is intended to support reading in the content area. The article indicates that traditional geometry does not suffice in describing many natural phenomena. The use of computers to implement repeated iterations can generate better models. Offered by IBM, this text can be used in a high school geometry class to demonstrate applications of similarity and to illustrate important ways that geometry can be used to model a wide range of scientific phenomena.

Type: Text Resource

Virtual Manipulative

Pupil Dilation:

This is an interactive model that demonstrates how different light levels effect the size of the pupil of the eye. Move the slider to change the light level and see how the pupil changes.

Type: Virtual Manipulative

Worksheet

The Koch Snowflake:

Students will analyze the perimeters of stages of the Koch Snowflake and note that the perimeter grows by a factor of 4/3 from one stage to the next. This means that the perimeter of this figure grows without bound even though its area is bounded. This effect was noted in the late 1800's and has been called the Coastline Paradox.

Type: Worksheet

MFAS Formative Assessments

Showing Similarity:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two quadrilaterals are similar.

The Consequences of Similarity:

Students are given the definition of similarity in terms of similarity transformations and are asked to explain how this definition ensures the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

To Be or Not To Be Similar:

Students are asked to use the definition of similarity in terms of similarity transformations to determine whether or not two triangles are similar.

Student Resources

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

Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Task

Are They Similar?:

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

Type: Problem-Solving Task

Parent Resources

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

Perspectives Video: Professional/Enthusiast

Making Candy: Uniform Scaling:

Don't be a shrinking violet. Learn how uniform scaling is important for candy production.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Task

Are They Similar?:

In this problem, students are given a picture of two triangles that appear to be similar, but whose similarity cannot be proven without further information. Asking students to provide a sequence of similarity transformations that maps one triangle to the other, using the definition of similarity in terms of similarity transformations.

Type: Problem-Solving Task