NY Next Generation Math GEO-G.SRT.2
The Standard
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar. Explain using similarity transformations that similar triangles have equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students decide whether figures are similar by finding a similarity transformation with a specified dilation center and scale factor plus rigid motions. They connect that mapping to equal corresponding angles and proportional corresponding sides.
What Mastery Looks Like
- The student gives a valid transformation sequence and matches corresponding vertices. The student verifies angle equality and one common side-length ratio.
Common Misconceptions
- Students may compare side differences instead of ratios or omit the dilation center. They may match angles and sides using inconsistent vertex correspondence.
How to Assess It
- Give two coordinate triangles. Ask students to decide similarity, specify a transformation sequence, and verify corresponding angles and side ratios.
Lesson moves
Ways to Teach It
Overlay traced figures after a specified dilation and rigid motions, then mark corresponding parts.
Ask why equal corresponding angles alone do not prove arbitrary polygons similar.
Play similarity mapping with vertex correspondences, centers, scale factors, and motion cards.
Verify similarity between two map outlines or scaled design drawings.
Keep exploring
Related Standards
- GEO-G.SRT.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of sine, cosine and tangent r...
- NY-8.G.5
Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transve...
- 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.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...
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