Geometry

Lessons

• 1 1.1 Drawing Conclusions
• 2 1.2 Conditional Statements
• 3 1.3 Equivalent Statements
• 4 1.4 Definitions
• 5 1.5 Valid and Invalid Deductions
• 6 1.6 Arguments with Two Premises
• 7 1.7 Direct Proof: Arguments with Several Premises
• 8 1.8 Indirect Proof
• 9 1.9 A Deductive System
• 10 2.1 Points, Lines, and Planes
• 11 2.2 The Ruler Postulate
• 12 2.3 Properties of Equality
• 13 2.4 Betweenness of Points
• 14 2.5 Line Segments
• 15 2.6 Polygons
• 16 3.1 Rays and Angles
• 17 3.2 The Protractor Postulate
• 18 3.3 Betweenness of Rays
• 19 3.4 Complementary and Supplementary Angles
• 20 3.5 Linear Pairs and Vertical Angles
• 21 3.6 Parallel and Perpendicular Lines
• 22 4.1 Triangles
• 23 4.2 Congruent Polygons
• 24 4.3 Proving Triangles Congruent
• 25 4.4 Proving Corresponding Parts Equal
• 26 4.5 The Isosceles Triangle Theorem
• 27 4.6 The S.S.S. Congruence Theorem
• 28 4.7 Construction
• 29 4.8 More Construction
• 30 5.1 Properties of Inequality
• 31 5.2 The Exterior Angle Theorem
• 32 5.3 Triangle Side and Angle Inequalities
• 33 5.4 The Triangle Inequality Theorem
• 34 6.1 Proving Lines Parallel
• 35 6.2 Perpendicular Lines
• 36 6.3 The Parallel Postulate
• 37 6.4 Some Consequences of the Parallel Postulate
• 38 6.5 More on Distance
• 39 6.6 The Angles of a Triangle
• 40 6.7 Two More Ways to Prove Triangles Congruent
• 41 7.1 Quadrilaterals
• 42 7.2 Parallelograms
• 43 7.3 Quadrilaterals That Are Parallelagrams
• 44 7.4 Rectangles, Rhombuses, and Squares
• 45 7.5 Trapezoids
• 46 7.6 The Midsegment Theorem
• 47 8.1 Reflections
• 48 8.2 Properties of Isometries
• 49 8.3 Translations
• 50 8.4 Rotations
• 51 8.5 Congruences and Isometries
• 52 8.6 Symmetry
• 53 9.1 Polygon Regions and Area
• 54 9.2 Squares and Rectangles
• 55 9.3 Triangles
• 56 9.4 Parallelograms and Trapezoids
• 57 9.5
• 58 9.6 Heron's Theorem
• 59 10.1 Similarity
• 60 10.2 The Side-Splitter Theorem
• 61 10.3 Similar Polygons
• 62 10.4 The A.A. Similarity Theorem
• 63 10.5 The S.A.S. Similarity Theorem
• 64 10.6 The Angle Bisector Theorem
• 65 11.1 Proportions in a Right Triangle
• 66 11.2 The Pythagorean Theorem Revisted
• 67 11.3 Isosceles and 3o°-60° Triangles
• 68 11.4 The Tangent Ratio
• 69 11.5 The Sine and Cosine Ratios
• 70 12.1 Circles, Radii, and Chords
• 71 12.2 Tangents
• 72 12.3 Central Angles and Arcs
• 73 12.4 Inscribed Angles
• 74 12.5 Secant Angles
• 75 12.6 Tangent Segments
• 76 12.7 Chords and Secant Segments
• 77 13.1 Concyclic Points
• 78 13.2 Cyclic Quadrilaterals
• 79 13.3 Incircles
• 80 13.4 Ceva's Theorem
• 81 13.5 The Centroid of a Triangle
• 82 13.6 Constructions
• 83 14.1 Regular Polygons
• 84 14.2 The Perimeter of a Regular Polygon
• 85 14.3 The Area of a Regular Polygon
• 86 14.4 Limits
• 87 14.5 The Circumference and Area of a Circle
• 88 14.6 Sectors and Arcs
• 89 15.1 Lines and Planes in Space
• 90 15.2 Rectangular Solids
• 91 15.3 Prisms
• 92 15.4 The Volume of a Prism
• 93 15.5 Pyramids
• 94 15.6 Cylinders and Cones
• 95 15.7 Spheres
• 96 15.8 Similar Solids
• 97 16.1 Geometry on a Sphere
• 98 16.2 The Saccheri Quadrilateral
• 99 16.3 The Geometries pf Lobachevsky and Riemann
• 100 16.4 The Triangle Angle Sum Theorem Revisted
• 101 17.1 Coordinate Systems
• 102 17.2 The Distance Formula
• 103 17.3 Slope
• 104 17.4 Parallel and Perpendicular Lines
• 105 17.5 The Midpoint Formula
• 106 17.6 Coordinate Proofs