Standard #: MAFS.912.G-SRT.1.2 (Archived Standard)


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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: 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 - Archived
Assessed: Yes

Test Item Specifications

    N/A

    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 # Question Difficulty Type
Sample Item 1

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.

 

 

N/A MS: Multiselect


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Related Resources

Formative Assessments

Name Description
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.

Lesson Plans

Name Description
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.

Transformation and Similarity

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

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.

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.
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.

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.

Perspectives Video: Professional/Enthusiast

Name Description
Making Candy: Uniform Scaling

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

Problem-Solving Tasks

Name Description
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.

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.

Text Resource

Name Description
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.

Virtual Manipulative

Name Description
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.

Worksheet

Name Description
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.

Student Resources

Perspectives Video: Professional/Enthusiast

Name Description
Making Candy: Uniform Scaling:

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

Problem-Solving Task

Name Description
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.



Parent Resources

Perspectives Video: Professional/Enthusiast

Name Description
Making Candy: Uniform Scaling:

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

Problem-Solving Task

Name Description
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.



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