CCSS.Math.Content.HSG-SRT.A
The standard
Understand similarity in terms of similarity transformations
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to see similarity as a result of transformations, especially dilations plus rigid motions. They should be able to describe how one figure maps onto another, name the scale factor, and explain why corresponding angles match while side lengths scale by the same ratio.
Mastery looks like students justifying similarity, not only spotting figures that look alike. They can use coordinates, diagrams, or transformation language to prove two triangles or polygons are similar. Common trouble spots are mixing up congruence and similarity, using the wrong side pair for scale factor, and assuming all stretched shapes are similar.
Ways to teach it
- Give pairs of paper triangles and have students dilate one from a marked center, then rotate or translate it onto the other.
- Ask students to write, “These figures are similar because…” using the words dilation, scale factor, and corresponding parts.
- Show two coordinate triangles and ask students to find one transformation sequence and the scale factor in three minutes.
- Have students compare two phone screenshots of the same photo at different sizes and explain why the images are similar.
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Related standards
- CCSS.Math.Content.HSG-SRT.A.2
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformatio...
- CCSS.Math.Content.HSG-SRT.A.3
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
- CCSS.Math.Content.HSG-SRT.B
Prove theorems involving similarity
- CCSS.Math.Content.8.G.A.4
Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translation...