CCSS.Math.Content.HSG-CO.B.6
The Standard
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.
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students describe how translations, rotations, and reflections move a figure without changing its size or shape. They use a sequence of these motions to determine whether one figure can map exactly onto another.
What Mastery Looks Like
- Students accurately describe translations, rotations, and reflections using vectors, centers, angles, or reflection lines. They map corresponding points and justify congruence by naming a valid sequence of rigid motions.
Common Misconceptions
- Students may think a figure is congruent after resizing because the shape looks the same. They may also confuse rotation direction, reflection lines, or the order of multiple motions. Some assume matching orientation is required for congruence.
How to Assess It
- Give two triangles on a coordinate grid. Ask students to decide whether they are congruent and describe a sequence of rigid motions that maps one onto the other.
Lesson moves
Ways to Teach It
Use tracing paper to slide, turn, and flip a polygon onto a second polygon, then record each motion in order.
Ask students to explain why a reflection changes orientation but does not change side lengths or angle measures.
Play a card-matching game where students pair preimages, images, and written descriptions of the rigid motions connecting them.
Compare two floor tile designs and identify the translations, rotations, or reflections that repeat one tile without changing its size or shape.
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Printable HSG-CO.B.6 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-CO.B.6, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.G.A.2
Students must already connect congruence with sequences of rotations, reflections, and translations to decide congruence using rigid motions.
- CCSS.Math.Content.8.G.A.1
Knowing rotations, reflections, and translations preserve size and shape is needed to use rigid motions to prove congruence.
- CCSS.Math.Content.HSG-CO.A.5
Drawing rigid motions and finding transformation sequences are needed to test whether one figure can be moved onto another.
What This Unlocks
Mastery here sets students up for these next.
- CCSS.Math.Content.HSG-SRT.A.2
Similarity transformations extend rigid-motion congruence by adding dilations, so students reuse mapping figures and matching corresponding parts.
- CCSS.Math.Content.HSG-CO.B.7
Students need rigid motion congruence to connect triangle side and angle matches with an actual motion mapping one triangle to another.
- CCSS.Math.Content.HSG-CO.B.8
Students must use rigid motions and the congruence definition before deriving why ASA, SAS, and SSS guarantee triangle congruence.
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