CCSS.Math.Content.HSG-CO.C

MathGrades 9–12Congruence

The standard

Prove geometric theorems

Common Core State Standards for Mathematics · High School — Geometry

What this standard means

Students need to use definitions, diagrams, and logical steps to prove geometry facts. They should connect earlier ideas about congruence, transformations, parallel lines, triangles, and quadrilaterals to make a convincing argument, not just give an answer.

Mastery looks like a clear proof with correct reasons for each claim. Students can choose a useful theorem, mark the diagram, and explain why the conclusion follows. Common sticking points are naming the right congruent parts, using a theorem before it has been proved, and writing reasons that are too vague.

Ways to teach it

  • Have students build two intersecting lines with patty paper, measure vertical angles, then write a proof for why they match.
  • Prompt students to explain which proof step is weakest in a sample triangle proof and rewrite it with a precise reason.
  • Give a four-step proof with missing reasons and ask students to fill them in on an index card.
  • Use a photo of roof trusses and ask students where congruent triangles would help justify equal lengths or angles.

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Related standards

Standard text verified against corestandards.org on July 10, 2026.

Page updated July 10, 2026.

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