CCSS.Math.Content.HSG-SRT.A.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 the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
Common Core State Standards for Mathematics
What this standard means
Students need to decide whether two figures are similar by thinking about transformations: translations, rotations, reflections, and dilations. They should be able to describe a sequence that maps one figure onto the other, or explain why no such sequence works.
Mastery looks like matching corresponding vertices, checking equal angles, and confirming side lengths have the same scale factor. Students often get stuck pairing the wrong sides, assuming figures are similar because they look alike, or using only one matching angle or side ratio as proof.
Ways to teach it
- Give pairs cut from grid paper and have students trace, slide, flip, rotate, and enlarge one figure to match the other.
- Ask students to write: How can you prove two triangles are similar without measuring every angle and side?
- Show two triangles with side lengths labeled and ask students to identify corresponding sides and decide if one scale factor works.
- Have students compare two differently sized phone screenshots and describe the dilation that keeps the image shape unchanged.
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Related standards
- CCSS.Math.Content.HSG-SRT.A
Understand similarity in terms of similarity transformations
- 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.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- 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...