CCSS.Math.Content.8.G.A.2
The standard
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.
Common Core State Standards for Mathematics · Geometry
What this standard means
Students need to see congruence as same size, same shape, reached by moving a figure without stretching or shrinking it. They should use translations, reflections, and rotations to map one figure onto another, then describe the steps in order using clear math language.
Mastery looks like naming a workable sequence, such as “reflect over the y-axis, then translate 3 units down,” and checking that all matching vertices land correctly. Students often get stuck with rotation direction, center of rotation, and mixing up “looks the same” with “maps exactly onto.”
Ways to teach it
- Have students cut out a triangle and physically slide, flip, and turn it onto a congruent triangle on grid paper.
- Ask students to write directions that move Figure A onto Figure B, then trade papers and test a partner’s directions.
- Show two congruent polygons on a coordinate grid and ask students to list one valid sequence of transformations on an exit ticket.
- Use a floor tile pattern and have students identify which tiles match by translation, reflection, or rotation.
Plan a lesson for CCSS.Math.Content.8.G.A.2
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Related standards
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Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and correspondin...
- CCSS.Math.Content.HSG-CO.B.6
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- CCSS.Math.Content.HSG-CO.A.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. ...
- CCSS.Math.Content.8.G.A.4
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translation...