MathBored

Virginia SOL Mathematics Textbook

Geometry

Aligned to the 2023 Virginia Mathematics Standards of Learning

This volume is still being written. Chapters 1–14 are complete and finished, and cover the circle standard G.PC.3 in full; the chapters still to come add equations of circles (G.PC.4) and three-dimensional figures (G.DF.1 and G.DF.2). The SOL coverage index lists exactly where every standard stands.

How to use this book SOL coverage index

Contents

  1. 1Logic, Conditionals, and Venn DiagramsG.RLT.1 (a, b, c, d)
    1. 1.1 Statements, Negation, and Compound Statements
    2. 1.2 Conditional Statements
    3. 1.3 Converse, Inverse, and Contrapositive
    4. 1.4 Biconditionals and Definitions
    5. 1.5 Venn Diagrams and Set Relationships

    WorkbookAnswer key

  2. 2Parallel Lines Cut by a TransversalG.RLT.2 (a, b, c)
    1. 2.1 The Transversal and Its Eight Angles
    2. 2.2 Proving the Angle Pair Relationships
    3. 2.3 Angle Chases, Numeric and Algebraic
    4. 2.4 Proving Lines Are Parallel
    5. 2.5 Parallel Lines in Context

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  3. 3Symmetry and TransformationsG.RLT.3 (a, b, c, d)
    1. 3.1 Lines of Symmetry
    2. 3.2 Line Symmetry and Point Symmetry
    3. 3.3 Translations and Reflections
    4. 3.4 Rotations and Dilations
    5. 3.5 Naming a Transformation from Its Image

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  4. 4Sides and Angles of a TriangleG.TR.1 (a, b, c, d, e)
    1. 4.1 The Angle Sum and the Exterior Angle
    2. 4.2 Ordering the Sides from the Angles
    3. 4.3 Ordering the Angles from the Sides
    4. 4.4 Does a Triangle Exist?
    5. 4.5 The Range for a Third Side, and Problems in Context

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  5. 5Proving Triangles CongruentG.TR.2 (a, d, e)
    1. 5.1 Congruent Triangles and Corresponding Parts
    2. 5.2 SSS and SAS
    3. 5.3 ASA and AAS
    4. 5.4 HL, and What Does Not Work
    5. 5.5 Direct and Indirect Proofs
    6. 5.6 Constructing a Congruent Triangle, and Measured Attributes

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  6. 6Congruence by Algebra and CoordinatesG.TR.2 (b, c, e)
    1. 6.1 Congruence from Algebra
    2. 6.2 Distance, Slope, and Midpoint
    3. 6.3 Coordinate Proofs of Congruence
    4. 6.4 Measured Attributes from Algebra and Coordinates

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  7. 7Proving Triangles SimilarG.TR.3 (a, b, c, d, e)
    1. 7.1 Similar Triangles, Correspondence, and Scale Factor
    2. 7.2 AA — Two Angles Are Enough
    3. 7.3 SSS Similarity and SAS Similarity
    4. 7.4 Similarity by Algebra
    5. 7.5 Similarity by Coordinates
    6. 7.6 Similarity as a Sequence of Transformations
    7. 7.7 Measured Attributes and Indirect Measurement

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  8. 8The Pythagorean Theorem and Special Right TrianglesG.TR.4 (a, b, c, f)
    1. 8.1 The Pythagorean Theorem
    2. 8.2 The Converse, and Classifying a Triangle
    3. 8.3 Pythagorean Triples
    4. 8.4 45°-45°-90° Triangles
    5. 8.5 30°-60°-90° Triangles

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  9. 9Right Triangle TrigonometryG.TR.4 (d, e, g)
    1. 9.1 Naming and Finding the Ratios
    2. 9.2 Verifying the Ratios
    3. 9.3 Finding a Missing Side
    4. 9.4 Finding a Missing Angle
    5. 9.5 Angles of Elevation and Depression

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  10. 10Properties of QuadrilateralsG.PC.1 (a, c, d)
    1. 10.1 The Six Families
    2. 10.2 Properties of Parallelograms
    3. 10.3 Rectangles and Rhombi
    4. 10.4 Squares, and What "Specific To" Means
    5. 10.5 Trapezoids and Isosceles Trapezoids
    6. 10.6 Constructions That Verify Properties

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  11. 11Quadrilaterals in the Coordinate PlaneG.PC.1 (a, b)
    1. 11.1 The Three Formulas
    2. 11.2 Proving a Parallelogram
    3. 11.3 Rectangles, Rhombi, and Squares
    4. 11.4 Trapezoids, and Choosing the Proof

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  12. 12Angles of Convex PolygonsG.PC.2 (a, b, c)
    1. 12.1 Convex Polygons and the Interior Angle Sum
    2. 12.2 Exterior Angles
    3. 12.3 Regular Polygons, One Angle at a Time
    4. 12.4 Working Backwards to $n$

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  13. 13Circles: Central and Inscribed AnglesG.PC.3 (b, c)
    1. 13.1 Circles and Arcs
    2. 13.2 Central Angles
    3. 13.3 Inscribed Angles
    4. 13.4 Three Consequences
    5. 13.5 Putting It Together

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  14. 14Circles: Arc Length and Sector AreaG.PC.3 (a, d, e)
    1. 14.1 The Fraction of a Circle
    2. 14.2 Arc Length
    3. 14.3 Sector Area
    4. 14.4 Putting It Together

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About this volume

Every chapter maps to specific Virginia SOL codes and closes with a coverage table showing where each Knowledge and Skill is taught and practiced. Standards marked by VDOE as assessed without a calculator are flagged in the chapters that cover them.

Standards text is drawn from the 2023 Mathematics Standards of Learning approved by the Virginia Board of Education on August 31, 2023. This book is an independent open resource and is not published or endorsed by the Virginia Department of Education.