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.

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

Multi-step Congruence

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CPALMS: Students are asked to describe a rigid motion to demonstrate two polygons are congruent.
Rigid Motion – 2
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CPALMS:Students are asked to explain congruence in terms of rigid motions.

Proving Congruence

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CPALMS: Students are asked to describe a rigid motion to demonstrate two polygons are congruent.
Rigid Motion – 3
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CPALMS: Students are asked to describe a rigid motion to demonstrate that two polygons are congruent.

Rigid Motion – 1

Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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CPALMS: This is a virtual realization of the physical experience when students are given 3 pieces of straws and are told to make them into a triangle. Students can determine unique triangles (SSS, SAS, ASA).

Congruent Triangles

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CPALMS: With this resource, the user can demonstrate or explore translation of shapes created with pattern blocks, using or not using a coordinate axes and lattice points background, by changing the translation vector.

Transformations – Translation

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CPALMS: The user clicks and drags a shape they have constructed to view its reflection across a line. A background grid and axes may or may not be used. The reflection may by examined analytically using coordinates. Symmetry may be displayed.

Transformations – Reflections

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CPALMS: With this resource, students can rotate shapes and their images with or without a background grid and axes.

Transformations – Rotation

Assessment Questions
Assessment Questions
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Multiple Choice
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Videos of Expert Instruction
Videos of Expert Instruction
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In this animated Math Shorts video, students will learn about translation, which occurs when a geometric shape slides from one location to another on a coordinate plane. The animation also explains mapping notations, which designate how far and in what direction a shape moves.

“Translation” by PBS Learning Media

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In this animated Math Shorts video, students learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. There is a class activity to support video.

“Rotation” by PBS Learning Media

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This animated video about reflection relates the geometric meaning of reflection to—a mirror image—and then displays geometric shapes on a coordinate plane reflecting through the x-axis and y-axis. There is a class activity to support video.

“Reflection” by PBS Learning Media

Hook/Performance Tasks
Hook/Performance Tasks
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Illustrative Mathematics: The purpose is to apply knowledge about triangles, circles, and squares in order to calculate and compare two different areas. This can be done several ways: the solutions given uses definition of congruence, the Pythagorean Theorem, and symmetry considerations.

Circle Sandwich

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Illustrative Mathematics: There are two goals: to develop student understanding of rigid motions in the context of demonstrating congruence, and student knowledge of reflections is refined by considering the notion of orientation.

Congruent Triangles

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Illustrative Mathematics: This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Congruent Rectangles

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Illustrative Mathematics: This task shows the congruence of two triangles in a particular geometric context arising by cutting a rectangle in half along the diagonal.

Cutting a Rectangle Into Two Congruent Triangles

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Illustrative Mathematics: By exhibiting a sequence of transformations that shows that two generic line segmanes of the same length oare congruent is a good way for students to begin thinking about transformations in greater generality.

Congruent Segments

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Illustrative Mathematics: Students have a chance to explore several issues relating to rigid motions of the plane and triangle congruence.

Triangle Congruence with Coordinates