NY Next Generation Math NY-8.G.4
The Standard
Know that a two-dimensional figure is similar to another if the corresponding angles are congruent and the corresponding sides are in proportion. Equivalently, two two-dimensional figures are similar if one is the image of the other after a sequence of rotations, reflections, translations, and dilations. Given two similar two-dimensional figures, describe a sequence that maps the similarity 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 similar figures through congruent corresponding angles and proportional corresponding sides. They describe coordinate transformations, including a specified dilation, that map one figure to the other.
What Mastery Looks Like
- The student verifies angle congruence and one consistent side-length scale factor. The student gives a valid sequence with a stated dilation center and scale factor.
Common Misconceptions
- Students may call figures similar because they look alike without checking proportions. They may use different scale factors for different sides or omit the dilation center.
How to Assess It
- Give two coordinate triangles with side scale factor 2. Ask students to verify similarity and describe a mapping sequence with a specified dilation center.
Lesson moves
Ways to Teach It
Use grid transparencies to map one polygon onto a scaled copy through rigid motions and dilation.
Ask students why equal angles alone establish similarity for triangles but not every polygon.
Play Similar or Not by checking corresponding angles and side ratios on figure cards.
Compare two scale drawings and identify the transformation sequence relating their coordinates.
Keep exploring
Related Standards
- NY-8.G.3
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- NY-8.G.2
Know that a two-dimensional figure is congruent to another if the corresponding angles are congruent and the corresponding sides are congruent. Equivalently, tw...
- 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...
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