CCSS.Math.Content.HSG-SRT.B
The standard
Prove theorems involving similarity
Common Core State Standards for Mathematics · High School — Geometry
What this standard means
Students need to use similarity as a proof tool, not just spot matching shapes. They should prove triangle relationships by using angle congruence, proportional sides, parallel lines, and scale factors. They also need to connect similarity to results like side-splitting, triangle proportionality, and relationships formed by an altitude to the hypotenuse.
Mastery looks like a clear proof with a diagram, marked givens, a chosen similarity statement in the correct order, and reasons for each step. Students often get stuck matching corresponding sides, writing proportions in the same order, or explaining why two triangles are similar before using the proportion.
Ways to teach it
- Have students cut a right triangle, draw the altitude to the hypotenuse, then match the three similar triangles with colored angle marks.
- Prompt students: Which triangles are similar in this diagram, and how do you know before using any side lengths?
- Give one diagram with parallel lines cutting triangle sides, and ask students to write one valid proportion and one proof reason.
- Use a map scale or phone photo enlargement to show how proving similarity justifies missing lengths without measuring directly.
Plan a lesson for CCSS.Math.Content.HSG-SRT.B
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSG-C.A.1
Prove that all circles are similar.
- 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-CO.C
Prove geometric theorems
- CCSS.Math.Content.HSG-SRT.B.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.