NY Next Generation Math NY-8.G.2
The Standard
Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, two two-dimensional figures are congruent if one is the image of the other after a sequence of rotations, reflections, and translations. Given two congruent figures, describe a sequence that maps the congruence between them on the coordinate plane.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify congruent figures by matching corresponding side lengths and angle measures. They also describe rotations, reflections, and translations that map one congruent figure onto another on a coordinate plane.
What Mastery Looks Like
- The student verifies all corresponding sides and angles, then gives a complete rigid-motion sequence with needed details. The mapped image lands exactly on the second figure without resizing.
Common Misconceptions
- Students may call figures congruent because they look alike or have equal area. They may include a dilation, omit a transformation detail, or match incorrect corresponding vertices.
How to Assess It
- Show two congruent triangles on a coordinate plane. Ask students to match vertices and describe a precise sequence of rigid motions mapping the first triangle onto the second.
Lesson moves
Ways to Teach It
Use tracing paper to translate, rotate, and reflect one polygon until it lands on a congruent partner.
Ask students why equal area alone does not prove that two figures are congruent.
Play rigid-motion sequence challenge with coordinate figures and transformation cards.
Verify whether two repeated tile or logo shapes are congruent and describe how one maps onto the other.
Keep exploring
Related Standards
- NY-8.G.4
Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, ...
- NY-8.G.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- NY-4.G.3
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Ide...
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.
Also for this standard:Make a WorksheetMake a QuizMake a Sub Lesson