Public learning track
Lines, Angles, and Geometric Constructions
9th Grade · Math · Open Global Math
13 lessons
Goal
Prove angle relationships involving intersecting and parallel lines and master classic Euclidean compass-and-straightedge constructions.
Featured Diagrams
Angle Pairs Review: Complementary, Supplementary, and Vertical Angles
13 lessons
0 of 13 done
- 1Angle Pairs Review: Complementary, Supplementary, and Vertical AnglesUp nextStart
- 2Angle Properties on Straight LinesPremiumNot started yet
- 3Angle Properties of Parallel Lines and TransversalsNot started yet
- 4Parallel Lines and Transversals: Alternate Interior and Exterior AnglesNot started yet
- 5Using Transversal Angle Relationships to Find Missing AnglesNot started yet
- 6Proving Lines Are Parallel Using Angle RelationshipsNot started yet
- 7Constructing the Perpendicular Bisector of a Line SegmentNot started yet
- 8Constructing an Angle Bisector with Compass and StraightedgeNot started yet
- 9Constructing a Perpendicular from a Point to a LineNot started yet
- 10Constructing a Perpendicular from an External PointNot started yet
- 11Constructing Parallel Lines Through an External PointNot started yet
- 12Constructing Regular Polygons: Equilateral Triangle and SquareNot started yet
- 13Using Constructions to Prove Geometric PropertiesNot started yet
Standards Covered
- OGM.10.GEO.1Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Establish 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.5Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Understand 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.3Open Global Math Standards 2026™ · Math · Level 10 / High School 1 (Age 14) · Grade 9Prove 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.
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.