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# 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
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 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 for a translation, and
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,
, for a 180-degree rotation about the origin,
, and for a 270-degree rotation about the origin,
. 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

#### Related Courses

 Course Number1111 Course Title222 1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) 1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated)) 7912070: Access Mathematics for Liberal Arts (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 - 2023, 2023 and beyond (current)) 1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current)) 1207300: Liberal Arts Mathematics 1 (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated)) 7912065: Access Geometry (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

#### 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.

#### 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.

 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.

#### 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.

 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.

#### 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.