NY Next Generation Math GEO-G.CO.7
The Standard
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 corresponding pairs of angles are congruent.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students connect triangle congruence by rigid motions with equality of all corresponding sides and angles. They prove both directions of this relationship.
What Mastery Looks Like
- The student identifies correct corresponding parts after a rigid-motion mapping and explains why their measures are equal. The student also uses equal corresponding parts to support congruence.
Common Misconceptions
- Students may match vertices by page position instead of correspondence or prove only one direction. They may cite equal area as enough for triangle congruence.
How to Assess It
- Give two labeled triangles and a proposed rigid-motion sequence. Ask students to verify correspondence and explain the if and only if statement in both directions.
Lesson moves
Ways to Teach It
Overlay traced triangles after rigid motions and mark every corresponding side and angle pair.
Ask why equal areas do not replace equal corresponding sides and angles.
Play correspondence match with triangle labels, rigid motions, and paired-part cards.
Verify whether two triangular manufactured pieces are congruent using a motion and measurements.
Keep exploring
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