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Scope and sequence · Math

Geometry

Euclid, proof and the measure of the world

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What to cover

59 of 73 lessons are MUST COVER. They are tested on the unit tests and exams, or are skills the SAT/ACT relies on. OPTIONAL lessons are enrichment. Do them if time allows. The course is complete when the MUST COVER lessons are done.

Unit 1: Foundations: Logic and the Axiomatic Method

  • OPTIONAL 1.1 Euclid's Elements and the Axiomatic Method
  • OPTIONAL 1.2 Inductive and Deductive Reasoning
  • MUST COVER 1.3 Conditional Statements · exam
  • MUST COVER 1.4 The Laws of Logic · exam
  • MUST COVER 1.5 Algebraic Proof and the Two-Column Format · exam

Unit 2: Points, Lines, Planes and Angles

  • OPTIONAL 2.1 Points, Lines and Planes
  • MUST COVER 2.2 Measuring and Constructing Segments · exam
  • OPTIONAL 2.3 Measuring Angles
  • MUST COVER 2.4 Angle Pairs and the Vertical Angles Theorem · exam
  • MUST COVER 2.5 Basic Constructions · exam
  • MUST COVER 2.6 Proving Statements About Segments and Angles · exam

Unit 3: Parallel and Perpendicular Lines

  • OPTIONAL 3.1 Lines, Transversals and Angle Pairs
  • MUST COVER 3.2 The Parallel Postulate and Parallel Lines · exam
  • MUST COVER 3.3 Proving Lines Parallel · exam
  • MUST COVER 3.4 Perpendicular Lines and Distance · exam
  • MUST COVER 3.5 Slopes of Parallel and Perpendicular Lines · exam, SAT/ACT

Unit 4: Triangles and Congruence

  • MUST COVER 4.1 Triangle Angle Sum and Exterior Angles · exam, SAT/ACT
  • MUST COVER 4.2 Congruent Figures · exam
  • MUST COVER 4.3 Proving Triangles Congruent: SSS and SAS · SAT/ACT
  • MUST COVER 4.4 Proving Triangles Congruent: ASA and AAS · exam, SAT/ACT
  • MUST COVER 4.5 Using Congruent Triangles (CPCTC) · exam, SAT/ACT
  • MUST COVER 4.6 Isosceles and Equilateral Triangles · exam, SAT/ACT
  • MUST COVER 4.7 Right Triangles: HL and Proofs with Two Pairs of Triangles · exam, SAT/ACT

Unit 5: Relationships Within Triangles

  • OPTIONAL 5.1 Perpendicular Bisectors and Angle Bisectors
  • MUST COVER 5.2 Circumcenter and Incenter · exam
  • MUST COVER 5.3 Medians, Altitudes and the Centroid · exam, SAT/ACT
  • MUST COVER 5.4 The Triangle Midsegment Theorem · SAT/ACT
  • MUST COVER 5.5 Indirect Proof and Inequalities in One Triangle · exam, SAT/ACT
  • MUST COVER 5.6 The Triangle Inequality and the Hinge Theorem · exam, SAT/ACT

Unit 6: Quadrilaterals and Polygons

  • MUST COVER 6.1 Angles of Polygons · exam
  • MUST COVER 6.2 Properties of Parallelograms · exam
  • OPTIONAL 6.3 Proving That a Quadrilateral Is a Parallelogram
  • MUST COVER 6.4 Rectangles, Rhombuses and Squares · exam
  • MUST COVER 6.5 Trapezoids and Kites · exam

Unit 7: Transformations

  • OPTIONAL 7.1 Translations and Vectors
  • MUST COVER 7.2 Reflections and Symmetry · exam
  • MUST COVER 7.3 Rotations and Rotational Symmetry · exam
  • OPTIONAL 7.4 Compositions and Congruence
  • MUST COVER 7.5 Dilations · exam

Unit 8: Similarity

  • MUST COVER 8.1 Ratios, Proportions and the Geometric Mean · SAT/ACT
  • OPTIONAL 8.2 Similar Polygons
  • MUST COVER 8.3 Proving Triangles Similar: AA · exam, SAT/ACT
  • MUST COVER 8.4 Proving Triangles Similar: SSS and SAS · SAT/ACT
  • MUST COVER 8.5 Proportions in Triangles · exam, SAT/ACT

Unit 9: Right Triangles and Trigonometry

  • MUST COVER 9.1 The Pythagorean Theorem and Its Proofs · SAT/ACT
  • MUST COVER 9.2 The Converse of the Pythagorean Theorem · SAT/ACT
  • MUST COVER 9.3 Similar Right Triangles and the Geometric Mean · exam, SAT/ACT
  • MUST COVER 9.4 Special Right Triangles · exam, SAT/ACT
  • MUST COVER 9.5 The Tangent Ratio · exam, SAT/ACT
  • MUST COVER 9.6 The Sine and Cosine Ratios · exam, SAT/ACT
  • MUST COVER 9.7 Angles of Elevation and Depression · exam

Unit 10: Circles

  • MUST COVER 10.1 Circles, Arcs and Central Angles · SAT/ACT
  • OPTIONAL 10.2 Chords
  • MUST COVER 10.3 Tangents · exam
  • MUST COVER 10.4 Inscribed Angles · exam
  • MUST COVER 10.5 Angles Formed by Chords, Secants and Tangents · exam
  • MUST COVER 10.6 Segment Lengths in Circles · exam, SAT/ACT
  • MUST COVER 10.7 Circles in the Coordinate Plane · exam, SAT/ACT

Unit 11: Area and Perimeter

  • MUST COVER 11.1 Areas of Rectangles, Parallelograms and Triangles · SAT/ACT
  • MUST COVER 11.2 Areas of Trapezoids, Rhombuses and Kites · SAT/ACT
  • MUST COVER 11.3 Areas of Regular Polygons · exam, SAT/ACT
  • OPTIONAL 11.4 Circumference and Arc Length
  • MUST COVER 11.5 Areas of Circles and Sectors · exam, SAT/ACT
  • MUST COVER 11.6 Areas of Similar Figures and Composite Regions · exam, SAT/ACT

Unit 12: Surface Area and Volume

  • OPTIONAL 12.1 Solids, Nets and Cross Sections
  • MUST COVER 12.2 Surface Area of Prisms and Cylinders · SAT/ACT
  • MUST COVER 12.3 Surface Area of Pyramids and Cones · SAT/ACT
  • MUST COVER 12.4 Volume of Prisms and Cylinders · SAT/ACT
  • MUST COVER 12.5 Volume of Pyramids and Cones · exam, SAT/ACT
  • MUST COVER 12.6 Spheres and Similar Solids · exam

Unit 13: Coordinate Geometry and Proof

  • MUST COVER 13.1 Coordinate Tools: Distance, Midpoint, Slope and Partitions · exam, SAT/ACT
  • OPTIONAL 13.2 Classifying Figures with Coordinates
  • MUST COVER 13.3 Coordinate Proofs · exam

36-week pacing calendar

From the course’s own 32-week pacing guide, with catch-up and review weeks added to fill a 36-week (180-day) year.

WeekPlanDoneNotes
Wk 1Day 1: Lesson 1.1 Euclid's Elements and the Axiomatic Method (day 1 of 2)
Day 2: Lesson 1.1 Euclid's Elements and the Axiomatic Method (day 2 of 2)
Day 3: Lesson 1.2 Inductive and Deductive Reasoning
Day 4: Lesson 1.3 Conditional Statements (day 1 of 2)
Day 5: Lesson 1.3 Conditional Statements (day 2 of 2)
Wk 2Day 1: Lesson 1.4 The Laws of Logic (day 1 of 2)
Day 2: Lesson 1.4 The Laws of Logic (day 2 of 2)
Day 3: Lesson 1.5 Algebraic Proof and the Two-Column Format (day 1 of 2)
Day 4: Lesson 1.5 Algebraic Proof and the Two-Column Format (day 2 of 2)
Day 5: Unit 1 review (mastery checklist and missed problems)
Wk 3Day 1: Unit 1 test
Day 2: Lesson 2.1 Points, Lines and Planes
Day 3: Lesson 2.2 Measuring and Constructing Segments (day 1 of 2)
Day 4: Lesson 2.2 Measuring and Constructing Segments (day 2 of 2)
Day 5: Lesson 2.3 Measuring Angles
Wk 4Day 1: Lesson 2.4 Angle Pairs and the Vertical Angles Theorem (day 1 of 2)
Day 2: Lesson 2.4 Angle Pairs and the Vertical Angles Theorem (day 2 of 2)
Day 3: Lesson 2.5 Basic Constructions (day 1 of 2)
Day 4: Lesson 2.5 Basic Constructions (day 2 of 2)
Day 5: Lesson 2.6 Proving Statements About Segments and Angles (day 1 of 2)
Wk 5Day 1: Lesson 2.6 Proving Statements About Segments and Angles (day 2 of 2)
Day 2: Unit 2 review (mastery checklist and missed problems)
Day 3: Unit 2 test
Day 4: Lesson 3.1 Lines, Transversals and Angle Pairs
Day 5: Lesson 3.2 The Parallel Postulate and Parallel Lines (day 1 of 2)
Wk 6Day 1: Lesson 3.2 The Parallel Postulate and Parallel Lines (day 2 of 2)
Day 2: Lesson 3.3 Proving Lines Parallel (day 1 of 2)
Day 3: Lesson 3.3 Proving Lines Parallel (day 2 of 2)
Day 4: Lesson 3.4 Perpendicular Lines and Distance (day 1 of 2)
Day 5: Lesson 3.4 Perpendicular Lines and Distance (day 2 of 2)
Wk 7Day 1: Lesson 3.5 Slopes of Parallel and Perpendicular Lines
Day 2: Unit 3 review (mastery checklist and missed problems)
Day 3: Unit 3 test
Day 4: Lesson 4.1 Triangle Angle Sum and Exterior Angles (day 1 of 2)
Day 5: Lesson 4.1 Triangle Angle Sum and Exterior Angles (day 2 of 2)
Wk 8Day 1: Lesson 4.2 Congruent Figures
Day 2: Lesson 4.3 Proving Triangles Congruent: SSS and SAS (day 1 of 2)
Day 3: Lesson 4.3 Proving Triangles Congruent: SSS and SAS (day 2 of 2)
Day 4: Lesson 4.4 Proving Triangles Congruent: ASA and AAS (day 1 of 2)
Day 5: Lesson 4.4 Proving Triangles Congruent: ASA and AAS (day 2 of 2)
Wk 9Day 1: Lesson 4.5 Using Congruent Triangles (CPCTC) (day 1 of 2)
Day 2: Lesson 4.5 Using Congruent Triangles (CPCTC) (day 2 of 2)
Day 3: Lesson 4.6 Isosceles and Equilateral Triangles (day 1 of 2)
Day 4: Lesson 4.6 Isosceles and Equilateral Triangles (day 2 of 2)
Day 5: Lesson 4.7 Right Triangles: HL and Proofs with Two Pairs of Triangles (day 1 of 2)
Wk 10Day 1: Lesson 4.7 Right Triangles: HL and Proofs with Two Pairs of Triangles (day 2 of 2)
Day 2: Unit 4 review (mastery checklist and missed problems)
Day 3: Unit 4 test
Day 4: Lesson 5.1 Perpendicular Bisectors and Angle Bisectors (day 1 of 2)
Day 5: Lesson 5.1 Perpendicular Bisectors and Angle Bisectors (day 2 of 2)
Wk 11Day 1: Lesson 5.2 Circumcenter and Incenter (day 1 of 2)
Day 2: Lesson 5.2 Circumcenter and Incenter (day 2 of 2)
Day 3: Lesson 5.3 Medians, Altitudes and the Centroid (day 1 of 2)
Day 4: Lesson 5.3 Medians, Altitudes and the Centroid (day 2 of 2)
Day 5: Lesson 5.4 The Triangle Midsegment Theorem
Wk 12Day 1: Lesson 5.5 Indirect Proof and Inequalities in One Triangle (day 1 of 2)
Day 2: Lesson 5.5 Indirect Proof and Inequalities in One Triangle (day 2 of 2)
Day 3: Lesson 5.6 The Triangle Inequality and the Hinge Theorem (day 1 of 2)
Day 4: Lesson 5.6 The Triangle Inequality and the Hinge Theorem (day 2 of 2)
Day 5: Unit 5 review (mastery checklist and missed problems)
Wk 13Day 1: Unit 5 test
Day 2: Lesson 6.1 Angles of Polygons
Day 3: Lesson 6.2 Properties of Parallelograms (day 1 of 2)
Day 4: Lesson 6.2 Properties of Parallelograms (day 2 of 2)
Day 5: Lesson 6.3 Proving That a Quadrilateral Is a Parallelogram (day 1 of 2)
Wk 14Day 1: Lesson 6.3 Proving That a Quadrilateral Is a Parallelogram (day 2 of 2)
Day 2: Lesson 6.4 Rectangles, Rhombuses and Squares (day 1 of 2)
Day 3: Lesson 6.4 Rectangles, Rhombuses and Squares (day 2 of 2)
Day 4: Lesson 6.5 Trapezoids and Kites (day 1 of 2)
Day 5: Lesson 6.5 Trapezoids and Kites (day 2 of 2)
Wk 15Day 1: Unit 6 review (mastery checklist and missed problems)
Day 2: Unit 6 test
Day 3: Midterm review (Units 1–6)
Day 4: Midterm exam (Units 1–6)
Day 5: Lesson 7.1 Translations and Vectors
Wk 16Day 1: Lesson 7.2 Reflections and Symmetry
Day 2: Lesson 7.3 Rotations and Rotational Symmetry (day 1 of 2)
Day 3: Lesson 7.3 Rotations and Rotational Symmetry (day 2 of 2)
Day 4: Lesson 7.4 Compositions and Congruence (day 1 of 2)
Day 5: Lesson 7.4 Compositions and Congruence (day 2 of 2)
Wk 17Catch-up and review week (no new lessons)
Wk 18Day 1: Lesson 7.5 Dilations (day 1 of 2)
Day 2: Lesson 7.5 Dilations (day 2 of 2)
Day 3: Unit 7 review (mastery checklist and missed problems)
Day 4: Unit 7 test
Day 5: Lesson 8.1 Ratios, Proportions and the Geometric Mean
Wk 19Day 1: Lesson 8.2 Similar Polygons
Day 2: Lesson 8.3 Proving Triangles Similar: AA (day 1 of 2)
Day 3: Lesson 8.3 Proving Triangles Similar: AA (day 2 of 2)
Day 4: Lesson 8.4 Proving Triangles Similar: SSS and SAS (day 1 of 2)
Day 5: Lesson 8.4 Proving Triangles Similar: SSS and SAS (day 2 of 2)
Wk 20Day 1: Lesson 8.5 Proportions in Triangles (day 1 of 2)
Day 2: Lesson 8.5 Proportions in Triangles (day 2 of 2)
Day 3: Unit 8 review (mastery checklist and missed problems)
Day 4: Unit 8 test
Day 5: Lesson 9.1 The Pythagorean Theorem and Its Proofs (day 1 of 2)
Wk 21Day 1: Lesson 9.1 The Pythagorean Theorem and Its Proofs (day 2 of 2)
Day 2: Lesson 9.2 The Converse of the Pythagorean Theorem
Day 3: Lesson 9.3 Similar Right Triangles and the Geometric Mean (day 1 of 2)
Day 4: Lesson 9.3 Similar Right Triangles and the Geometric Mean (day 2 of 2)
Day 5: Lesson 9.4 Special Right Triangles (day 1 of 2)
Wk 22Day 1: Lesson 9.4 Special Right Triangles (day 2 of 2)
Day 2: Lesson 9.5 The Tangent Ratio (day 1 of 2)
Day 3: Lesson 9.5 The Tangent Ratio (day 2 of 2)
Day 4: Lesson 9.6 The Sine and Cosine Ratios (day 1 of 2)
Day 5: Lesson 9.6 The Sine and Cosine Ratios (day 2 of 2)
Wk 23Day 1: Lesson 9.7 Angles of Elevation and Depression (day 1 of 2)
Day 2: Lesson 9.7 Angles of Elevation and Depression (day 2 of 2)
Day 3: Unit 9 review (mastery checklist and missed problems)
Day 4: Unit 9 test
Day 5: Lesson 10.1 Circles, Arcs and Central Angles
Wk 24Day 1: Lesson 10.2 Chords (day 1 of 2)
Day 2: Lesson 10.2 Chords (day 2 of 2)
Day 3: Lesson 10.3 Tangents (day 1 of 2)
Day 4: Lesson 10.3 Tangents (day 2 of 2)
Day 5: Lesson 10.4 Inscribed Angles (day 1 of 2)
Wk 25Day 1: Lesson 10.4 Inscribed Angles (day 2 of 2)
Day 2: Lesson 10.5 Angles Formed by Chords, Secants and Tangents (day 1 of 2)
Day 3: Lesson 10.5 Angles Formed by Chords, Secants and Tangents (day 2 of 2)
Day 4: Lesson 10.6 Segment Lengths in Circles (day 1 of 2)
Day 5: Lesson 10.6 Segment Lengths in Circles (day 2 of 2)
Wk 26Day 1: Lesson 10.7 Circles in the Coordinate Plane (day 1 of 2)
Day 2: Lesson 10.7 Circles in the Coordinate Plane (day 2 of 2)
Day 3: Unit 10 review (mastery checklist and missed problems)
Day 4: Unit 10 test
Day 5: Lesson 11.1 Areas of Rectangles, Parallelograms and Triangles
Wk 27Day 1: Lesson 11.2 Areas of Trapezoids, Rhombuses and Kites (day 1 of 2)
Day 2: Lesson 11.2 Areas of Trapezoids, Rhombuses and Kites (day 2 of 2)
Day 3: Lesson 11.3 Areas of Regular Polygons (day 1 of 2)
Day 4: Lesson 11.3 Areas of Regular Polygons (day 2 of 2)
Day 5: Lesson 11.4 Circumference and Arc Length (day 1 of 2)
Wk 28Day 1: Lesson 11.4 Circumference and Arc Length (day 2 of 2)
Day 2: Lesson 11.5 Areas of Circles and Sectors (day 1 of 2)
Day 3: Lesson 11.5 Areas of Circles and Sectors (day 2 of 2)
Day 4: Lesson 11.6 Areas of Similar Figures and Composite Regions (day 1 of 2)
Day 5: Lesson 11.6 Areas of Similar Figures and Composite Regions (day 2 of 2)
Wk 29Day 1: Unit 11 review (mastery checklist and missed problems)
Day 2: Unit 11 test
Day 3: Lesson 12.1 Solids, Nets and Cross Sections
Day 4: Lesson 12.2 Surface Area of Prisms and Cylinders (day 1 of 2)
Day 5: Lesson 12.2 Surface Area of Prisms and Cylinders (day 2 of 2)
Wk 30Day 1: Lesson 12.3 Surface Area of Pyramids and Cones (day 1 of 2)
Day 2: Lesson 12.3 Surface Area of Pyramids and Cones (day 2 of 2)
Day 3: Lesson 12.4 Volume of Prisms and Cylinders (day 1 of 2)
Day 4: Lesson 12.4 Volume of Prisms and Cylinders (day 2 of 2)
Day 5: Lesson 12.5 Volume of Pyramids and Cones (day 1 of 2)
Wk 31Day 1: Lesson 12.5 Volume of Pyramids and Cones (day 2 of 2)
Day 2: Lesson 12.6 Spheres and Similar Solids (day 1 of 2)
Day 3: Lesson 12.6 Spheres and Similar Solids (day 2 of 2)
Day 4: Unit 12 review (mastery checklist and missed problems)
Day 5: Unit 12 test
Wk 32Day 1: Lesson 13.1 Coordinate Tools: Distance, Midpoint, Slope and Partitions
Day 2: Lesson 13.2 Classifying Figures with Coordinates (day 1 of 2)
Day 3: Lesson 13.2 Classifying Figures with Coordinates (day 2 of 2)
Day 4: Lesson 13.3 Coordinate Proofs (day 1 of 2)
Day 5: Lesson 13.3 Coordinate Proofs (day 2 of 2)
Wk 33Day 1: Unit 13 review (mastery checklist and missed problems)
Day 2: Unit 13 test
Day 3: Final review (Units 1–6)
Day 4: Final review (Units 7–13)
Day 5: Final exam (Units 1–13)
Wk 34Catch-up week: finish any MUST COVER lesson not yet done
Wk 35Catch-up week: finish any MUST COVER lesson not yet done
Wk 36Year-end review, portfolio and records

Grading: Daily practice sets 20%, Unit tests 50%, Midterm exam 15%, Final exam 15%. Scale: A 90–100, B 80–89, C 70–79, D 60–69, below 60 redo