CCSS.Math.Content.HSG-C.A.3
The standard
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Common Core State Standards for Mathematics
What this standard means
Students need to construct the incircle and circumcircle of a triangle using angle bisectors and perpendicular bisectors. They should know which center each construction finds, why it works, and how the radius is chosen.
Mastery means students can make accurate compass and straightedge constructions, explain each step, and prove facts about cyclic quadrilaterals, especially that opposite angles are supplementary. Students often mix up incenter and circumcenter, use the wrong bisectors, or remember the angle rule without linking it to intercepted arcs.
Ways to teach it
- Have students use compass and straightedge to construct both circles for the same triangle, then label the incenter, circumcenter, and radii.
- Ask students to explain why opposite angles in an inscribed quadrilateral add to 180 degrees using arcs, not memorized rules.
- Give a four-question exit ticket: identify the needed bisectors, find a missing angle, and choose the correct circle center from a diagram.
- Show a photo of a triangular park or sign, then ask where to place one sprinkler to reach all three vertices equally.
Plan a lesson for CCSS.Math.Content.HSG-C.A.3
Generate a complete lesson plan aligned to this standard, with objectives, activities, and materials. Free, no account needed.
Related standards
- CCSS.Math.Content.HSG-CO.C.9
Prove theorems about lines and angles.
- CCSS.Math.Content.HSG-CO.C.10
Prove theorems about triangles.
- CCSS.Math.Content.HSG-SRT.B.4
Prove theorems about triangles.
- CCSS.Math.Content.HSG-CO.D.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.