# MAFS.912.G-CO.2.6

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
General Information
Subject Area: Mathematics
Domain-Subdomain: Geometry: Congruence
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence in terms of rigid motions. (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
Assessed: Yes
Test Item Specifications
Also assesses:

MAFS.912.G-CO.2.7

MAFS.912.G-CO.2.8

• 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.

Items must not use matrices to describe transformations.

Items must not require the student to use the distance formula.

Items may require the student to find the distance between two
points or the slope of a line.

In items that require the student to represent transformations, at
least two transformations should be applied

• Calculator :

Neutral

• Clarification :
Students will use rigid motions to transform figures.

Students will predict the effect of a given rigid motion on a given
figure.

Students will use the definition of congruence in terms of rigid
motions to determine if two figures are congruent.

Students will explain triangle congruence using the definition of
congruence in terms of rigid motions.

Students will apply congruence to solve problems.

Students will use congruence to justify steps within the context of a
proof.

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

Items may require the student to determine the rigid motions that
show that two triangles are congruent.

• Response Attributes :
Items may ask the student to name corresponding angles and/or
sides.

Items may require the student to use a function, e.g.,

y=k(f(x+a))+b , to describe a transformation.

In items in which the student must write the line of reflection, any
line may be used.

Items may require the student to be familiar with slope-intercept
form of a line, standard form of a line, and point-slope form of a line.

Items may require the student to name corresponding angles or
sides.

Items may require the student to determine the transformations
required to show a given congruence.

Items may require the student to list sufficient conditions to prove
triangles are congruent.

Items may require the student to determine if given information is
sufficient for congruence.

Items may require the student to give statements to complete formal
and informal proofs.

Sample Test Items (1)
• Test Item #: Sample Item 1
• Question:

Evelyn is designing a pattern for a quilt using polygon EQFRGSHP shown.

Evelyn transforms EQFRGSHP so that the impage of E is at (2,0) and the image of R is at (6,-7). Which transformation could Evelyn have used to show EQFRGSHP and its image are congruent?

• Difficulty: N/A
• Type: MC: Multiple Choice

## 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))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
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-CO.2.AP.6a: Use descriptions of rigid motion and transformed geometric figures to predict the effects rigid motion has on figures in the coordinate plane.
MAFS.912.G-CO.2.AP.6b: Knowing that rigid transformations preserve size and shape or distance and angle, use this fact to connect the idea of congruency and develop the definition of congruent.

## Related Resources

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

## Assessments

Sample 4 - High School Geometry State Interim Assessment:

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

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

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

Type: Assessment

## Educational Software / Tool

Transformations Using Technology:

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Type: Educational Software / Tool

## Formative Assessments

Congruent Trapezoids:

Students will determine whether two given trapezoids are congruent.

Type: Formative Assessment

Transform This:

Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.

Type: Formative Assessment

Repeated Reflections and Rotations:

Students are asked to describe what happens to a triangle after repeated reflections and rotations.

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

Where Will I Land?:

This is a beginning level lesson on predicting the effect of a series of reflections or a quick review of reflections for high school students.

Type: Lesson Plan

How do your Air Jordans move?:

In this inquiry lesson, students are moving their individually designed Air Jordans around the room to explore rigid transformations on their shoes. They will Predict-Observe-Explain the transformations and then have to explain their successes/failures to other students.

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

Transformers 3:

Lesson is introduced by teacher activating students' prior knowledge of congruence. The teacher will present the power point that defines and illustrates transformations by rigid motion. The students will answer questions on their worksheets at the time indicated in the power point. The students will work on their independent assignment. The teacher will give a short quiz to test for understanding. The teacher will assign for the students to take pictures of the three transformations found in the real world.

Type: Lesson Plan

Reflections and Isosceles Triangles:

This activity uses rigid transformations of the plane to explore symmetries of classes of triangles.

Reflections and Equilateral Triangles:

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles

Building a tile pattern by reflecting octagons:

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

Building a tile pattern by reflecting hexagons:

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.

## MFAS Formative Assessments

Congruent Trapezoids:

Students will determine whether two given trapezoids are congruent.

Repeated Reflections and Rotations:

Students are asked to describe what happens to a triangle after repeated reflections and rotations.

Transform This:

Students are asked to translate and rotate a triangle in the coordinate plane and explain why the pre-image and image are congruent.

## Student Resources

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

## Educational Software / Tool

Transformations Using Technology:

This virtual manipulative can be used to demonstrate and explore the effect of translation, rotation, and/or reflection on a variety of plane figures. A series of transformations can be explored to result in a specified final image.

Type: Educational Software / Tool

Reflections and Isosceles Triangles:

This activity uses rigid transformations of the plane to explore symmetries of classes of triangles.

Reflections and Equilateral Triangles:

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles

Building a tile pattern by reflecting octagons:

This task applies reflections to a regular octagon to construct a pattern of four octagons enclosing a quadrilateral: the focus of the task is on using the properties of reflections to deduce that the quadrilateral is actually a square.

Building a tile pattern by reflecting hexagons:

This task applies reflections to a regular hexagon to construct a pattern of six hexagons enclosing a seventh: the focus of the task is on using the properties of reflections to deduce this seven hexagon pattern.

## Parent Resources

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

Reflections and Isosceles Triangles:

This activity uses rigid transformations of the plane to explore symmetries of classes of triangles.

Reflections and Equilateral Triangles:

This activity is one in a series of tasks using rigid transformations of the plane to explore symmetries of classes of triangles, with this task in particular focusing on the class of equilaterial triangles