Jacobs Geometry
Contents 21 sections

Teacher’s Guide for Geometry: Seeing, Doing, Understanding

Harold R. Jacobs — Teacher’s Guide (W. H. Freeman), converted from the scanned PDF Teacher's Guide_LessonPlans.pdf into Markdown and split by chapter.

The guide has two parts, both included here:

  1. Lesson plans (lesson-plans/) — one file per chapter, with each numbered lesson (outline, list of transparencies, introduction, and teaching notes).
  2. Notes on the chapters (notes/) — Peter Renz’s chapter-by-chapter commentary (printed pages 414–482).

How figures are handled

The source is a page scan, so no figure could be copied as a vector image. Each transparency, worksheet, and in-text diagram was instead located on the page and cropped to a JPEG in figures/ — 367 images in all. They are referenced inline:

![Transparency 5-4-1: Quadrilateral inequality](../figures/p045-5.jpg)
*Transparency 5-4-1: Quadrilateral inequality*

The file name gives the PDF page (p045 = 45th page of the PDF) and the figure’s position on that page. Captions combine the transparency number with the title given in the lesson’s transparency list. Where a figure has no printed number, the caption describes the diagram.

Every page begins with an anchor such as <a id="page-293"></a>, and the printed page number (293) is used throughout, so any passage can be checked against the PDF.

Lesson plans

Introduction: Euclid, the Surfer and the Spotter

  • Section introduction (no numbered lessons)

Chapter 1: An Introduction to Geometry

  • Lesson 1: Lines in Designing a City
  • Lesson 2: Angles in Measuring the Earth
  • Lesson 3: Polygons and Polyhedra: Pyramid Architecture
  • Lesson 4: Constructions: Telling Time with Shadows
  • Lesson 5: We Can’t Go On Like This
  • Review of Chapter 1

Chapter 2: The Nature of Deductive Reasoning

  • Lesson 1: Conditional Statements
  • Lesson 2: Definitions
  • Lesson 3: Direct Proof
  • Lesson 4: Indirect Proof
  • Lesson 5: A Deductive System
  • Lesson 6: Some Famous Theorems of Geometry
  • Review of Chapter 2

Chapter 3: Lines and Angles

  • Lesson 1: Number Operations and Equality
  • Lesson 2: The Ruler and Distance
  • Lesson 3: The Protractor and Angle Measure
  • Lesson 4: Bisection
  • Lesson 5: Complementary and Supplementary Angles
  • Lesson 6: Linear Pairs and Vertical Angles
  • Lesson 7: Perpendicular and Parallel Lines
  • Review of Chapter 3

Chapter 4: Congruence

  • Lesson 1: Coordinates and Distance
  • Lesson 2: Polygons and Congruence
  • Lesson 3: ASA and SAS Congruence
  • Lesson 4: Congruence Proofs
  • Lesson 5: Isosceles and Equilateral Triangles
  • Lesson 6: SSS Congruence
  • Lesson 7: Constructions
  • Review of Chapter 4

Chapter 5: Inequalities

  • Lesson 1: Properties of Inequality
  • Lesson 2: The Exterior Angle Theorem
  • Lesson 3: Triangle Side and Angle Inequalities
  • Lesson 4: The Triangle Inequality Theorem
  • Review of Chapter 5

Chapter 6: Parallel Lines

  • Lesson 1: Line Symmetry
  • Lesson 2: Proving Lines Parallel
  • Lesson 3: The Parallel Postulate
  • Lesson 4: Parallel Lines and Angles
  • Lesson 5: The Angles of a Triangle
  • Lesson 6: AAS and HL Congruence
  • Review of Chapter 6

Chapter 7: Quadrilaterals

  • Lesson 1: Quadrilaterals
  • Lesson 2: Parallelograms and Point Symmetry
  • Lesson 3: More on Parallelograms
  • Lesson 4: Rectangles, Rhombuses, and Squares
  • Lesson 5: Trapezoids
  • Lesson 6: The Midsegment Theorem
  • Review of Chapter 7

Chapter 8: Transformations

  • Lesson 1: Transformations
  • Lesson 2: Reflections
  • Lesson 3: lsometries and Congruence
  • Lesson 4: Transformations and Symmetry
  • Review of Chapter 8

Chapter 9: Area

  • Lesson 1: Area
  • Lesson 2: Squares and Rectangles
  • Lesson 3: Triangles
  • Lesson 4: Parallelograms and Trapezoids
  • Lesson 5: The Pythagorean Theorem
  • Review of Chapter 9

Chapter 10: Similarity

  • Lesson 1: Ratio and Proportion
  • Lesson 2: Similar Figures
  • Lesson 3: The Side-Splitter Theorem
  • Lesson 4: The AA Similarity Theorem
  • Lesson 5: Proportions and Dilations
  • Lesson 6: Perimeters and Areas of Similar Figures
  • Review of Chapter 10

Chapter 11: The Right Triangle

  • Lesson 1: Proportions in a Right Triangle
  • Lesson 2: The Pythagorean Theorem Revisited
  • Lesson 3: Isosceles and 30°-60° Right Triangles
  • Lesson 4: The Tangent Ratio
  • Lesson 5: The Sine and Cosine Ratios
  • Lesson 6: Slope
  • Lesson 7: The Laws of Sines and Cosines
  • Review of Chapter 11

Chapter 12: Circles

  • Lesson 1: Circles, Radii, and Chords
  • Lesson 2: Tangents
  • Lesson 3: Central Angles and Arcs
  • Lesson 4: Inscribed Angles
  • Lesson 5: Secant Angles
  • Lesson 6: Tangent Segments and Intersecting Chords
  • Review of Chapter 12

Chapter 13: The Concurrence Theorems

  • Lesson 1: Triangles and Circles
  • Lesson 2: Cyclic Quadrilaterals
  • Lesson 3: Incircles
  • Lesson 4: The Centroid of a Triangle
  • Lesson 5: Ceva’s Theorem
  • Lesson 6: Napoleon’s Discovery and Other Surprises
  • Review of Chapter 13

Chapter 14: Regular Polygons and the Circle

  • Lesson 1: Regular Polygons
  • Lesson 2: The Perimeter of a Regular Polygon
  • Lesson 3: The Area of a Regular Polygon
  • Lesson 4: From Polygons to Pi
  • Lesson 5: The Area of a Circle
  • Lesson 6: Sectors and Arcs
  • Review of Chapter 14

Chapter 15: Geometric Solids

  • Lesson 1: Lines and Planes in Space
  • Lesson 2: Rectangular Solids
  • Lesson 3: Prisms
  • Lesson 4: The Volume of a Prism
  • Lesson 5: Pyramids
  • Lesson 6: Cylinders and Cones
  • Lesson 7: Spheres
  • Lesson 8: Similar Solids
  • Lesson 9: The Regular Polyhedra
  • Review of Chapter 15

Chapter 16: Non-Euclidean Geometries

  • Lesson 1: Geometry on a Sphere
  • Lesson 2: The Saccheri Quadrilateral
  • Lesson 3: The Geometries of Lobachevsky and Riemann
  • Lesson 4: The Triangle Angle Sum Theorem Revisited
  • Review of Chapter 16

Notes on each chapter

Also included: LessonPlans-complete.md, the same material in a single file.

Transcription notes

  • Text comes from the PDF’s OCR layer, checked against the page images and corrected where it was clearly wrong (for example dzrect → “direct”, AABC → “△ABC”).
  • Geometry symbols used: △ triangle, ∠ angle, ≅ congruent, ∼ similar, ∥ parallel, ⊥ perpendicular, ≈ approximately, √ square root, α area, π pi.
  • Fractions that were typeset as stacked fractions are written on one line, e.g. 23/80 = 33/x.
  • The prose is reliable throughout. Dense mathematical displays — chiefly in the supplementary notes for Chapters 11 and 14–16 — are the hardest thing for OCR, and a few equations remain approximate; the page anchors make it easy to check them against the scanned page.