CCSS.Math.Content.HSG-CO.C.10
The standard
Prove theorems about triangles.
Common Core State Standards for Mathematics
What this standard means
Students need to prove key triangle facts using definitions, diagrams, prior theorems, and logical steps. They should explain why triangle angles add to 180, why isosceles base angles match, why a midsegment is parallel and half as long, and why medians meet at one point.
Mastery looks like a clear proof with correct reasons, not just a correct picture or measurement. Students often get stuck choosing a useful construction, naming congruent parts precisely, or linking parallel lines, angle relationships, and triangle congruence in order.
Ways to teach it
- Hands-on activity: Have students cut out paper triangles, tear off the three corners, and line them up to form a straight angle.
- Discussion prompt: Ask, "What extra line could we draw to make this triangle proof easier, and why would that line help?"
- Quick assessment: Give a diagram of an isosceles triangle and ask students to write a two-column proof that the base angles are congruent.
- Real-world connection: Use a roof truss photo and ask students to identify midpoint segments, medians, and congruent triangle parts in the structure.
Plan a lesson for CCSS.Math.Content.HSG-CO.C.10
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Related standards
- CCSS.Math.Content.HSG-CO.C.9
Prove theorems about lines and angles.
- 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.