OGM.10.GEO
Open Global Math Standards 2026™ · 9th Grade
Geometric Properties, Deductive Proof, Constructions, and Transformations
Grade9th Grade
SubjectMath
Levelstrand
Child standards (8)
- OGM.10.GEO.1Establish geometric primitives (points, lines, planes, angles), prove angle theorems (vertical angles, complementary/supplementary angles, parallel lines cut by a transversal), and execute compass and straightedge constructions.
- OGM.10.GEO.2Prove triangle theorems (interior/exterior angles, triangle inequality, medians/centroid, mid-segments) and establish triangle congruence criteria (SAS, ASA, SSS, AAS, HL) using deductive logic.
- OGM.10.GEO.3Prove and apply properties and classification criteria of quadrilaterals and general polygons (parallelograms, rectangles, rhombi, squares, trapezoids, regular polygons), including angle sum formulas and tessellation conditions.
- OGM.10.GEO.4Investigate and prove circle theorems: perpendicular bisector of a chord, inscribed angle theorem and its corollaries, cyclic quadrilaterals, tangents and secants, and tangent segment lengths from an external point.
- OGM.10.GEO.5Understand mathematical proof structure: distinguish between definitions, axioms, conjectures, theorems, and converses; construct direct synthetic proofs, proofs by contradiction (proof by contradiction), and use counterexamples.
- OGM.10.GEO.6Apply rigid transformations (translations, reflections, rotations) and homothetic dilations to plane figures; analyze line symmetry and rotational symmetry; and determine coordinates of transformed shapes.
- OGM.10.GEO.7Prove and apply similarity criteria for triangles (AA, SAS, SSS similarity) and Thales' Parallel Projection Theorem; establish that area ratios of similar figures scale as the square of the similarity ratio; and explore the Golden Ratio.
- OGM.10.GEO.8Locate points and calculate distances, midpoints, and gradients in the Cartesian plane; use bearings and distance coordinates; and relate 3D objects to orthographic projections (plans/elevations) and nets.