CCSS.Math.Content.HSG-SRT.A.3
The standard
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Common Core State Standards for Mathematics
What this standard means
Students need to show why two triangles are similar when two pairs of angles match. They should connect angle preservation under rotations, reflections, translations, and dilations to a formal argument. The main idea is that if two angles match, the third angle must match too, and a dilation can resize one triangle to fit the other.
Mastery looks like a clear sequence of transformations, not just saying “same shape.” Students often get stuck thinking equal angles prove congruence, or they skip the dilation step. They may also name matching vertices in the wrong order, which breaks the argument.
Ways to teach it
- Give pairs of cut-out triangles with two marked angles, and have students transform and dilate one onto the other on grid paper.
- Ask students to write: Why do two equal angle pairs force the third angle pair to be equal too?
- Show two triangles with angle markings, and ask students to state whether AA similarity applies and name corresponding vertices.
- Use a phone map zoom example to discuss how dilation changes lengths but keeps angles the same.
Plan a lesson for CCSS.Math.Content.HSG-SRT.A.3
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Related standards
- CCSS.Math.Content.8.G.A.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...
- 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.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- CCSS.Math.Content.HSG-SRT.B
Prove theorems involving similarity