OGM.11.GEO
Open Global Math Standards 2026™ · 10th Grade
Geometry: Logical Foundations, Axiomatic Proofs, Transformations, and Coordinate Geometry
Grade10th Grade
SubjectMath
Levelstrand
Child standards (7)
- OGM.11.GEO.1Understand undefined terms (point, line, plane, distance), definitions, postulates, and conditional statements (converse, inverse, contrapositive, biconditionals); verify conjectures or provide counterexamples, and compare Euclidean and non-Euclidean/spherical geometries.
- OGM.11.GEO.2Perform formal geometric constructions (copying segments/angles, bisecting, parallel and perpendicular lines, tangent lines, regular inscribed polygons) using compass and straightedge or dynamic geometric software, and use constructions to formulate and test geometric conjectures.
- OGM.11.GEO.3Define rigid motions (translations, reflections, rotations) and dilations as functions in the coordinate plane; determine symmetries of 2D shapes; analyze compositions of transformations; establish criteria for congruence (SSS, SAS, ASA, AAS, HL) and similarity (AA, SAS, SSS) based on transformations.
- OGM.11.GEO.4Prove and apply theorems regarding lines, angles (vertical, parallel transversal angles, perpendicular bisectors), triangles (interior/exterior angle sum, isosceles base angles, midsegments, medians, concurrency, triangle inequality), quadrilaterals (parallelograms, rectangles, rhombuses, squares, trapezoids), and proportional relationships (triangle proportionality, geometric mean with right triangle altitudes).
- OGM.11.GEO.5Prove and apply theorems concerning circles (similarity of circles, relationships among central, inscribed, circumscribed angles, radii, chords, secants, tangents, and inscribed quadrilaterals); construct inscribed and circumscribed circles of triangles.
- OGM.11.GEO.6Use coordinate algebra to derive distance, midpoint, and partition formulas of directed line segments; write equations of parallel and perpendicular lines; derive standard and general equations of circles, parabolas, ellipses, and hyperbolas; and prove geometric properties on the coordinate plane.
- OGM.11.GEO.7Represent vectors in 2D Euclidean space geometrically and algebraically; perform vector addition, subtraction, scalar multiplication, and calculate vector magnitude; apply vectors to solve geometric problems and proofs.