CCSS.Math.Content.HSG-CO.A.5

MathGrades 9–12Congruence

The standard

Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

Common Core State Standards for Mathematics

What this standard means

Students need to move figures accurately using translations, rotations, and reflections. They should be able to draw the image on graph paper, tracing paper, or geometry software, then describe the move using clear details like direction, distance, line of reflection, center, and angle of rotation.

Mastery looks like matching every point of a figure to its correct image and explaining the transformation without guessing. Students often mix up clockwise and counterclockwise rotations, reflect over the wrong line, or describe a translation too vaguely, like saying “move it over” without units or direction.

Ways to teach it

  • Give students a triangle on graph paper and have them translate it 4 right and 3 down, then label each image point.
  • Ask students to write directions that move Figure A onto Figure B, using exact transformation language a partner can follow.
  • Show one preimage and three possible images, then ask students to identify which one matches a reflection over the y-axis.
  • Have students use a phone photo editing app to describe a crop rotation, mirror flip, or slide as a geometric transformation.

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Related standards

  • CCSS.Math.Content.HSG-CO.A.2

    Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as...

  • CCSS.Math.Content.HSG-CO.A.3

    Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

  • CCSS.Math.Content.8.G.A.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 trans...

  • 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...

Standard text verified against corestandards.org on July 10, 2026.

Page updated July 10, 2026.

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