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| Module 1: Congruence, Proof, and Constructions |
| Lessons 1 & 2: Construct an Equilateral Triangle |
| Lesson 3: Copy and Bisect an Angle |
| Lesson 4: Construct a Perpendicular Bisector |
| Lesson 5: Points of Concurrencies |
| Lesson 6: Solve for Unknown Angles—Angles and Lines at a Point |
| Lesson 7: Solve for Unknown Angles—Transversals |
| Lesson 8: Solve for Unknown Angles—Angles in a Triangle |
| Lesson 9: Unknown Angle Proofs—Writing Proofs |
| Lesson 10: Unknown Angle Proofs—Proofs with Constructions |
| Lesson 11: Unknown Angle Proofs—Proofs of Known Facts |
| Lesson 12: Transformations—The Next Level |
| Lesson 13: Rotations |
| Lesson 14: Reflections |
| Lesson 15: Rotations, Reflections, and Symmetry |
| Lesson 16: Translations |
| Lesson 17: Characterize Points on a Perpendicular Bisector |
| Lesson 18: Looking More Closely at Parallel Lines |
| Lesson 19: Construct and Apply a Sequence of Rigid Motions |
| Lesson 20: Applications of Congruence in Terms of Rigid Motions |
| Lesson 21: Correspondence and Transformations |
| Lesson 22: Congruence Criteria for Triangles—SAS |
| Lesson 23: Base Angles of Isosceles Triangles |
| Lesson 24: Congruence Criteria for Triangles—ASA and SSS |
| Lesson 25: Congruence Criteria for Triangles—AAS and HL |
| Lessons 26 & 27: Triangle Congruency Proofs |
| Lesson 28: Properties of Parallelograms |
| Lesson 29: Special Lines in Triangles |
| Lesson 30: Special Lines in Triangles |
| Lesson 31: Construct a Square and a Nine-Point Circle |
| Lesson 32: Construct a Nine-Point Circle |
| Lessons 33 & 34: Review of the Assumptions |
| Module 2: Similarity, Proof, and Trigonometry |
| Lesson 1: Scale Drawings |
| Lesson 2: Making Scale Drawings Using the Ratio Method |
| Lesson 3: Making Scale Drawings Using the Parallel Method |
| Lesson 4:Comparing the Ratio Method with the Parallel Method |
| Lesson 5: Scale Factors |
| Lesson 6: Dilations as Transformations of the Plane |
| Lesson 7: How Do Dilations Map Segments? |
| Lesson 8: How Do Dilations Matp Lines, Rays, and Circles? |
| Lesson 9: How Do Dilations Map Angles? |
| Lesson 10: Dividing the King’s Foot into 12 Equal Pieces |
| Lesson 11: Dilations from Different Centers |
| Lesson 12: What Are Similarity Transformations, and Why Do We Need Them? |
| Lesson 13: Properties of Similarity Transformations |
| Lesson 14: Similarity |
| Lesson 15: The Angle-Angle (AA) Criterion for Two Triangles to Be Similar |
| Lesson 16: Between-Figure and Within-Figure Ratios |
| Lesson 17: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to Be Similar |
| Lesson 18: Similarity and the Angle Bisector Theorem |
| Lesson 19: Families of Parallel Lines and the Circumference of the Earth |
| Lesson 20: How Far Away Is the Moon? |
| Lesson 21: Special Relationships Within Right Triangles—Dividing into Two Similar Sub-Triangles |
| Lesson 22: Multiplying and Dividing Expressions with Radicals |
| Lesson 23: Adding and Subtracting Expressions with Radicals |
| Lesson 24: Prove the Pythagorean Theorem Using Similarity |
| Lesson 25: Incredibly Useful Ratios |
| Lesson 26: The Definition of Sine, Cosine, and Tangent |
| Lesson 27: Sine and Cosine of Complementary Angles and Special Angles |
| Lesson 28: Solving Problems Using Sine and Cosine |
| Lesson 29: Applying Tangents |
| Lesson 30: Trigonometry and the Pythagorean Theorem |
| Lesson 31: Using Trigonometry to Determine Area |
| Lesson 32: Using Trigonometry to Find Side Lengths of an Acute Triangle |
| Lesson 33: Applying the Laws of Sines and Cosines |
| Lesson 34: Unknown Angles |
| Module 3: Extending to Three Dimensions |
| Lesson 1: What Is Area? |
| Lesson 2: Properties of Area |
| Lesson 3: The Scaling Principle for Area |
| Lesson 4: Proving the Area of a Disk |
| Lesson 5: Three-Dimensional Space |
| Lesson 6: General Prisms and Cylinders and Their Cross-Sections |
| Lesson 7: General Pyramids and Cones and Their Cross-Sections |
| Lesson 8: Definition and Properties of Volume |
| Lesson 9: Scaling Principle for Volumes |
| Lesson 10: The Volume of Prisms and Cylinders and Cavalieri’s Principle |
| Lesson 11: The Volume Formula of a Pyramid and Cone |
| Lesson 12: The Volume Formula of a Sphere |
| Lesson 13: How Do 3D Printers Work? |
| Module 4: Connecting Algebra and Geometry Through Coordinates |
| Lesson 1: Searching a Region in the Plane |
| Lesson 2: Finding Systems of Inequalities That Describe Triangular and Rectangular Regions |
| Lesson 3: Lines That Pass Through Regions |
| Lesson 4: Designing a Search Robot to Find a Beacon |
| Lesson 5: Criterion for Perpendicularity |
| Lesson 6: Segments That Meet at Right Angles |
| Lesson 7: Equations for Lines Using Normal Segments |
| Lesson 8: Parallel and Perpendicular Lines |
| Lesson 9: Perimeter and Area of Triangles in the Cartesian Plane |
| Lesson 10: Perimeter and Area of Polygonal Regions in the Cartesian Plane |
| Lesson 11: Perimeters and Areas of Polygonal Regions Defined by Systems of Inequalities |
| Lesson 12: Dividing Segments Proportionately |
| Lesson 13: Analytic Proofs of Theorems Previously Proved by Synthetic Means |
| Lesson 14: Motion Along a Line—Search Robots Again |
| Lesson 15: The Distance from a Point to a Line |
| Module 5: Circles With and Without Coordinates |
| Lesson 1: Thales’ Theorem |
| Lesson 2: Circles, Chords, Diameters, and Their Relationships |
| Lesson 3: Rectangles Inscribed in Circles |
| Lesson 4: Experiments with Inscribed Angles |
| Lesson 5: Inscribed Angle Theorem and Its Applications |
| Lesson 6: Unknown Angle Problems with Inscribed Angles in Circles |
| Lesson 7: The Angle Measure of an Arc |
| Lesson 8: Arcs and Chords |
| Lesson 9: Arc Length and Areas of Sectors |
| Lesson 10: Unknown Length and Area Problems |
| Lesson 11: Properties of Tangents |
| Lesson 12: Tangent Segments |
| Lesson 13: The Inscribed Angle Alternate—A Tangent Angle |
| Lesson 14: Secant Lines; Secant Lines That Meet Inside a Circle |
| Lesson 15: Secant Angle Theorem, Exterior Case |
| Lesson 16: Similar Triangles in Circle-Secant (or Circle-Secant-Tangent) Diagrams |
| Lesson 17: Writing the Equation for a Circle |
| Lesson 18: Recognizing Equations of Circles |
| Lesson 19: Equations for Tangent Lines to Circles |
| Lesson 20: Cyclic Quadrilaterals |
| Lesson 21: Ptolemy’s Theorem |