Protected instructional resource

Printable Teacher Answer Keys

Each student lesson has a corresponding key with the same diagrams, final answers, and concise reasoning.

Unit 01 · Foundations, Constructions & Geometric Reasoning

Points, Lines, Planes & Defined Terms

Segments, Rays, Angles & Notation

Distance, Midpoint & Segment Partition

Compass-and-Straightedge Constructions

Conditional Statements, Converses & Counterexamples

Two-Column, Flow & Paragraph Proofs

Unit 02 · Transformations, Symmetry & Congruence

Translations on the Coordinate Plane

Reflections Across Axes and Lines

Rotations About the Origin and Other Centers

Compositions of Transformations

Rigid Motion Definition of Congruence

Line, Rotational & Point Symmetry

Tessellations, Frieze Patterns & Design Rules

Unit 03 · Triangle Congruence & Proof

Triangle Classification & Angle Relationships

SSS and SAS Congruence

ASA, AAS and HL Congruence

CPCTC and Multi-Step Triangle Proofs

Isosceles and Equilateral Triangle Theorems

Triangle Inequality & Feasible Construction

Perpendicular Bisectors, Angle Bisectors & Centers

Unit 04 · Parallel Lines, Slopes & Coordinate Proof

Parallel Lines Cut by a Transversal

Proving Lines Parallel from Angle Relationships

Slope as Direction and Rate

Parallel and Perpendicular Slopes

Coordinate Proof with Distance, Midpoint & Slope

Equations of Lines in Geometric Context

Unit 05 · Similarity, Dilations & Proportional Reasoning

Dilations from a Center

Similarity Through Transformations

AA Similarity and Triangle Proportions

SSS and SAS Similarity

Side-Splitter and Proportional Segments

Scale Drawings, Maps & Models

Indirect Measurement, Shadows & Mirrors

Unit 06 · Right Triangles, Trigonometry & Bearings

Pythagorean Theorem & Its Converse

Special Right Triangles: 45-45-90

Special Right Triangles: 30-60-90

Geometric Mean & Right-Triangle Altitudes

Sine, Cosine & Tangent Ratios

Inverse Trigonometry & Angle Measure

Angles of Elevation and Depression

Bearings, Vectors & Multi-Step Navigation

Unit 07 · Polygons & Quadrilaterals

Interior and Exterior Angles of Polygons

Parallelogram Properties & Tests

Rectangles, Rhombi & Squares

Trapezoids, Kites & Midsegments

Quadrilateral Coordinate Proofs

Regular Polygons, Apothem & Central Angles

Polygon Decomposition & Design Constraints

Unit 08 · Circles, Arcs & Tangency

Circle Vocabulary, Radius, Diameter & Chords

Central Angles, Arcs & Arc Length

Inscribed Angles & Intercepted Arcs

Chords, Perpendicular Bisectors & Distances

Tangents and Radius Relationships

Secant, Chord & Tangent Power Theorems

Sector Area, Segment Area & Annuli

Equation of a Circle & Coordinate Applications

Unit 09 · Analytic Geometry, Loci & Conic Connections

Locus as a Set of Points Meeting a Condition

Perpendicular and Angle Bisector Loci

Distance from a Point to a Line

Coordinate Intersections and Geometric Systems

Circle-Line Intersections and Tangency

Parabolas as Distance Loci

Voronoi Thinking, Nearest-Point Regions & Design

Unit 10 · Area, Measurement & Geometric Probability

Area of Triangles, Parallelograms & Trapezoids

Area of Regular Polygons and Composite Figures

Heron’s Formula and Coordinate Area

Effects of Scale on Perimeter and Area

Units, Precision, Error & Significant Figures

Geometric Probability by Length and Area

Optimization with Perimeter and Area Constraints

Unit 11 · Solids, Surface Area & Volume

Prisms, Cylinders & Cavalieri’s Principle

Pyramids and Cones

Spheres: Surface Area and Volume

Nets and Surface Area of Prisms and Pyramids

Surface Area of Cylinders and Cones

Cross-Sections and Solids of Revolution

Similarity, Scale and Volume Relationships

Unit 12 · CAD, Scale Drawing & Spatial Design

CAD Workspace, Units, Grid and Snap

Precision Lines, Angles and Dimensions

Layers, Objects and Geometric Organization

Scale Plans, Rooms and Openings

Area, Perimeter and Material Schedules

Transformations, Repetition and Modular Design

Export, Print/PDF, SVG, DXF and Design Defense

Unit 13 · Geometry Modeling Capstone & Defense

Frame a Geometric Design or Investigation

Develop Constructions, Models and Proof

Test Measurements, Sensitivity and Limitations

Prepare a Printable Technical Portfolio

Present, Defend and Revise the Design

Final Synthesis, Examination and Completion Record