NY Next Generation Math GEO-G.C.1

MathGrades 9–12Understand and apply theorems about circles.

The Standard

Prove that all circles are similar.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students prove that any circle can be mapped to any other circle by a similarity transformation. They use a translation and dilation based on the centers and radii.
What Mastery Looks Like: The student maps one center to the other and chooses the ratio of radii as the scale factor. The argument explains why every point on the first circle lands on the second.
Common Misconceptions: Students may claim circles are similar only when their radii match or use an additive radius change. They may omit the centers from the transformation argument.
How to Assess It: Give two circles with different centers and radii. Ask students to describe a similarity transformation and justify its scale factor.

Lesson moves

Trace two circles on transparencies, align their centers, and dilate one tracing to match the other.
Ask why the ratio of radii, rather than their difference, determines the dilation.
Play transformation sequence with center, translation, and scale-factor cards for circle pairs.
Explain why circular logos remain similar when resized for different signs.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.