CCSS.Math.Content.HSG-CO.A.1
The standard
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Common Core State Standards for Mathematics
What this standard means
Students need to use exact geometry definitions, not just pictures or rough descriptions. They should explain angles, circles, perpendicular lines, parallel lines, and segments using point, line, and distance ideas. They also need to spot when a definition is too vague or depends only on how a diagram looks.
Mastery looks like writing and using definitions that work in any diagram. Students can sort examples from nonexamples and defend their choices with precise language. Common trouble spots are saying parallel lines “never touch” without saying coplanar, treating a segment like a whole line, or defining a circle as a “round shape” instead of a set of points at a fixed distance.
Ways to teach it
- Give students definition cards and diagram cards, then have them match, revise, and justify each pairing with a partner.
- Ask students to write the best possible definition of a circle, then trade papers and test it against weird examples.
- Show five diagrams and ask students to label each as example or nonexample, with one sentence explaining why.
- Have students find parallel lines, perpendicular lines, segments, angles, and circles in a classroom photo, then describe each precisely.
Plan a lesson for CCSS.Math.Content.HSG-CO.A.1
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Related standards
- CCSS.Math.Content.HSG-C.A
Understand and apply theorems about circles
- CCSS.Math.Content.4.MD.C
Geometric measurement: understand concepts of angle and measure angles.
- CCSS.Math.Content.HSG-CO.A.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
- CCSS.Math.Content.4.G.A.1
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.