Public learning track
Transformations, Symmetries, and Dilations in the Plane
9th Grade · Math · Open Global Math
5 lessons
Goal
Apply rigid motions, homothety/dilations, analyze rotational and reflectional symmetries, and calculate coordinate mappings.
Featured Diagrams
Rigid Plane Motions: Translations, Reflections, and Rotations
5 lessons
0 of 5 done
- 1Rigid Plane Motions: Translations, Reflections, and RotationsUp nextStart
- 2Line Symmetry, Rotational Symmetry, and Point SymmetryPremiumNot started yet
- 3Translations, Reflections, and Rotations on the Coordinate PlaneNot started yet
- 4Homothetic Dilations and Scale Factors from a CenterNot started yet
- 5Compositions of Transformations and Glide ReflectionsNot started yet
Standards Covered
- OGM.10.GEO.6Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Apply 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.8Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Locate 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.
- OGM.10.GEO.7Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Prove 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.
Curriculum Framework
9th Grade · Math · Open Global Math
1
7 lessons
Geometric Reasoning, Axiomatic Systems, and Proof Methods
Understand the logical architecture of geometry and construct rigorous direct proofs, indirect proofs, and counterexamples.
2
13 lessons
Lines, Angles, and Geometric Constructions
Prove angle relationships involving intersecting and parallel lines and master classic Euclidean compass-and-straightedge constructions.
3
8 lessons
Triangle Theorems and Deductive Properties
Prove fundamental triangle theorems including angle sums, inequalities, medians, centroids, and mid-segments.
4
8 lessons
Triangle Congruence Criteria and Synthetic Proofs
Establish triangle congruence criteria (SAS, ASA, SSS, AAS, HL) and construct rigorous geometric proofs of triangle properties.
5
7 lessons
Properties and Proofs of Quadrilaterals and Polygons
Prove classification properties of special quadrilaterals, derive polygon angle sum formulas, and analyze tessellation conditions.
6
9 lessons
Similarity, Proportions, and Dilations
Prove and apply triangle similarity criteria, Thales' Theorem, area scaling laws, and explore the Golden Ratio.
7
7 lessons
Circle Theorems: Chords, Angles, and Cyclic Quadrilaterals
Prove circle theorems involving chords, central and inscribed angles, angles in the same segment, and cyclic quadrilaterals.
8
7 lessons
Tangents, Secants, and Circle Power Theorems
Prove tangent theorems, alternate segment theorem, power of a point, and execute circle tangent constructions.
9
5 lessons
Transformations, Symmetries, and Dilations in the Plane
Apply rigid motions, homothety/dilations, analyze rotational and reflectional symmetries, and calculate coordinate mappings.
10
8 lessons
Coordinate Geometry, Bearings, and Spatial Representations
Calculate coordinate distances, midpoints, slopes, navigate using three-figure bearings, and interpret 3D orthographic views and nets.