Unit 1
Geometric Foundations & Reasoning
- Points, lines, planes and segments
- Angles and angle relationships
- Parallel and perpendicular lines
- Definitions, postulates and theorems
- Precision in geometric notation
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School Mathematics · Grades 6–12
Geometry
A rigorous geometry pathway built around transformations, congruence, similarity, proof, right-triangle trigonometry, circles, coordinate geometry, measurement, and modeling.
Course overview
The roadmap follows the Wisconsin high-school geometry structure: students move from visual and transformational reasoning into formal proof, similarity, trigonometry, circles, analytic geometry, measurement, and applications.
Math Aficionado uses this structure as a tutoring roadmap rather than a fixed school syllabus. Lessons can be reordered around the student's current unit, teacher materials, placement level, assignments, and assessment goals.
Units & topics
Unit 2
Transformations & Symmetry
- Translations, rotations and reflections
- Dilations and scale factor
- Coordinate rules for transformations
- Symmetry and composition of transformations
- Using transformations to reason about figures
Unit 3
Congruence & Triangle Structure
- Triangle classification
- Congruence criteria: SSS, SAS, ASA and AAS
- Corresponding parts
- Triangle inequality and special segments
- Applications of congruent triangles
Unit 4
Proof, Constructions & Geometric Argument
- Conditional statements and converses
- Two-column, paragraph and flow proofs
- Proofs involving lines, angles and triangles
- Compass-and-straightedge constructions
- Using diagrams as evidence without relying on appearance
Unit 5
Similarity & Proportional Geometry
- Similarity transformations
- AA, SAS and SSS similarity
- Proportional sides and scale factors
- Similar triangles and indirect measurement
- Applications to maps, models and design
Unit 6
Right Triangles & Trigonometry
- Pythagorean Theorem and converse
- Special right triangles
- Sine, cosine and tangent
- Solving right triangles
- Angle of elevation/depression and modeling
Unit 7
Quadrilaterals & Polygon Geometry
- Parallelograms and their properties
- Rectangles, rhombi and squares
- Trapezoids and kites
- Interior and exterior angle relationships
- Coordinate proofs of quadrilateral properties
Unit 8
Coordinate & Analytic Geometry
- Distance and midpoint
- Slope and equations of lines
- Perpendicular and parallel relationships
- Coordinate proofs
- Area and perimeter using coordinates
Unit 9
Circles
- Circle vocabulary and equations
- Central and inscribed angles
- Chords, tangents and secants
- Arc length and sector area
- Cyclic quadrilaterals and circle modeling
Unit 10
Conics & Geometric Equations
- Equations of circles
- Completing the square
- Parabolas and geometric definitions
- Ellipse and hyperbola concepts
- Connecting algebraic and geometric descriptions
Unit 11
Measurement & Three-Dimensional Geometry
- Area and perimeter
- Surface area and volume
- Cylinders, cones and spheres
- Cross-sections and nets
- Composite figures and dimensional reasoning
Unit 12
Geometry Modeling & Cumulative Proof
- Design and optimization problems
- Geometric modeling with constraints
- Choosing synthetic versus analytic methods
- Technology-assisted investigation
- Cumulative review and algebra/trigonometry connections
How the roadmap is aligned
Wisconsin Standards for Mathematics (2021), High School Geometry: Congruence; Similarity, Right Triangles & Trigonometry; Circles; Geometric Properties; Measurement; and Modeling.
This is an independent tutoring roadmap, not an official UW–Madison or Wisconsin Department of Public Instruction course. Wisconsin standards are used as the K–12 framework; current UW–Madison course descriptions are used where the pathway overlaps with college-level precalculus and calculus preparation.
Wisconsin Standards for Mathematics (2021) · UW–Madison Mathematics Course Guide
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