MAFS.8.G.1.2

Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
General Information
Subject Area: Mathematics
Grade: 8
Domain-Subdomain: Geometry
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Understand congruence and similarity using physical models, transparencies, or geometry software. (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 Assessed:

    MAFS.8.G.1.1 Verify experimentally the properties of rotations, reflections, and translations:

    MAFS.8.G.1.1a Lines are taken to lines, and line segments to line segments of the same length.

    MAFS.8.G.1.1b Angles are taken to angles of the same measure.

    MAFS.8.G.1.1c Parallel lines are taken to parallel lines.

  • Assessment Limits :
    The coordinate plane should not be used until MAFS.8.G.1.3. Limit sequences to no more than two transformations. A pre-image and image should not include apostrophe notation as this would give away the identification of similarity and congruence. No reference to the definition of congruence or symbols relating to the definition should be used (HS Geometry).
  • Calculator :

    Neutral

  • Context :

    Allowable

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question:

    Triangle ABC and its transformation DEF are shown.

    What transformation of triangle ABC produced triangle DEF?

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

  • Test Item #: Sample Item 2
  • Question:

    Select all the sequences of transformations that always maintain congruence.

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

Related Courses

This benchmark is part of these courses.
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.8.G.1.AP.2a: Demonstrate that two-dimensional polygons that are rotated, reflected, or translated are still congruent using area, perimeter, and length of sides on a coordinate plane.

Related Resources

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

Assessments

Sample 4 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 3 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 2 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth grade.

Type: Assessment

Sample 1 - Eighth Grade Math State Interim Assessment:

This is a State Interim Assessment for eighth 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

Proving Congruence:

Students are asked to explain congruence in terms of rigid motions.

Type: Formative Assessment

Multistep Congruence:

Students are asked to describe a sequence of rigid motions to demonstrate the congruence of two polygons.

Type: Formative Assessment

Rigid Motion - 3:

Students are asked to describe a rigid motion to demonstrate two polygons are congruent.

Type: Formative Assessment

Rigid Motion - 2:

Students are asked to describe a rigid motion to demonstrate two polygons are congruent.

Type: Formative Assessment

Rigid Motion - 1:

Students are asked to describe a rigid motion to demonstrate that two polygons are congruent.

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

"Triangle Congruence Show" Starring Rigid Transformations:

Students will be introduced to the definition of congruence in terms of rigid motion and use it to determine if two triangles are congruent.

Type: Lesson Plan

Triangles on a Lattice:

In this activity, students will use a 3x3 square lattice to study transformations of triangles whose vertices are part of the lattice. The tasks include determining whether two triangles are congruent, which transformations connect two congruent triangles, and the number of non-congruent triangles (with vertices on the lattice) that are possible.

Type: Lesson Plan

Identifying Similar Triangles:

This 105-minute lesson series helps teachers assess how students reason about geometry, including how they use facts about the angle sum and exterior angles of triangles to calculate missing angles, apply angle theorems to parallel lines cut by a transversal, and interpret geometrical diagrams using mathematical properties to identify similarity of triangles. In order to complete this lesson, students will need whiteboards, pens, wipes, copies of the assessment tasks, pencils, markers, scissors, glue sticks, and poster paper.

Type: Lesson Plan

Polygon Transformers:

This guided discovery lesson introduces students to the concept that congruent polygons can be formed using a series of transformations (translations, rotations, reflections). As a culminating activity, students will create a robot out of transformed figures.

Type: Lesson Plan

Triangles on a Lattice:

In this activity, students will use a 3x3 square lattice to study transformations of triangles whose vertices are part of the lattice. The tasks include determining whether two triangles are congruent, which transformations connect two congruent triangles, and the number of non-congruent triangles (with vertices on the lattice) that are possible.

Type: Lesson Plan

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Congruent Segments:

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

Congruent Triangles:

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorials

Rotating polygons 180 degrees about their center:

Students will investigate symmetry by rotating polygons 180 degrees about their center.

Type: Tutorial

Introduction to Transformations:

This video introduces the concept of rigid transformation and congruent figures.

Type: Tutorial

MFAS Formative Assessments

Multistep Congruence:

Students are asked to describe a sequence of rigid motions to demonstrate the congruence of two polygons.

Proving Congruence:

Students are asked to explain congruence in terms of rigid motions.

Rigid Motion - 1:

Students are asked to describe a rigid motion to demonstrate that two polygons are congruent.

Rigid Motion - 2:

Students are asked to describe a rigid motion to demonstrate two polygons are congruent.

Rigid Motion - 3:

Students are asked to describe a rigid motion to demonstrate two polygons 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

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Congruent Segments:

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

Congruent Triangles:

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task

Student Center Activity

Edcite: Mathematics Grade 8:

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

Tutorials

Rotating polygons 180 degrees about their center:

Students will investigate symmetry by rotating polygons 180 degrees about their center.

Type: Tutorial

Introduction to Transformations:

This video introduces the concept of rigid transformation and congruent figures.

Type: Tutorial

Parent Resources

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

Problem-Solving Tasks

Partitioning a Hexagon:

The purpose of this task is for students to find a way to decompose a regular hexagon into congruent figures. This is meant as an instructional task that gives students some practice working with transformations.

Type: Problem-Solving Task

Congruent Segments:

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

Type: Problem-Solving Task

Congruent Triangles:

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b). Each time the plane is reflected about a line, this reverses the notions of ''clockwise'' and ''counterclockwise.''

Type: Problem-Solving Task

Triangle congruence with coordinates:

In this resource, students will decide how to use transformations in the coordinate plane to translate a triangle onto a congruent triangle. Exploratory examples are included to prompt analytical thinking.

Type: Problem-Solving Task