CCSS.Math.Content.HSG-CO.C.9
The standard
Prove theorems about lines and angles.
Common Core State Standards for Mathematics
What this standard means
Students need to build logical proofs about angle relationships, not just name them. They should use diagrams, given information, definitions, and earlier results to prove facts about vertical angles, angles formed by parallel lines and a transversal, and perpendicular bisectors.
Mastery looks like a clear chain of reasons, with no missing steps. Students can mark a diagram, choose a useful theorem or definition, and explain why each statement follows. Common sticking points are mixing up alternate interior and corresponding angles, assuming lines are parallel without proof, and saying “they look equal” instead of giving a reason.
Ways to teach it
- Hands-on activity: Use patty paper to trace two intersecting lines, fold to match vertical angles, then write a two-column proof.
- Prompt: Explain why alternate interior angles are congruent only when the two crossed lines are parallel.
- Quick assessment: Give one marked diagram and ask students to fill in three missing reasons in a proof.
- Real-world connection: Use a photo of a ladder crossing parallel shelf edges and identify corresponding and alternate interior angles.
Plan a lesson for CCSS.Math.Content.HSG-CO.C.9
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Related standards
- CCSS.Math.Content.HSG-CO.C.10
Prove theorems about triangles.
- CCSS.Math.Content.HSG-CO.C
Prove geometric theorems
- CCSS.Math.Content.HSG-CO.C.11
Prove theorems about parallelograms.
- CCSS.Math.Content.HSG-SRT.B.4
Prove theorems about triangles.