# Geometry

True to traditional Geometry courses, topics include definitions, postulates, theorems, two-column proofs (mostly involving parallel lines and triangles), quadrilaterals, other polygons, circles, basic constructions, perimeter, area, solids, volume, surface area, analytic geometry and the basic trigonometric ratios. Geometry is taken either between or after the algebras in the sequence of courses. [There is no particular advantage either way.]

• 1.1  Sets, Statements and Reasoning
• 1.2  Informal Geometry and Measurement
• 1.3  Early Definitions and Postulates
• 1.4  Angles and Their Relationships
• 1.5  Introduction to Geometric Proof
• 1.6  Relationships: Perpendicular Lines
• 1.7  The Formal Proof of a Theorem
• 2.1  The Parallel Postulate and Special Angles
• 2.2  Indirect Proof
• 2.3  Proving Lines Parallel
• 2.4  The Angles of a Triangle
• 2.5  Convex Polygons
• 2.6  Symmetry and Transformations
• 3.1  Congruent Triangles
• 3.2  Corresponding Parts of Congruent Triangles
• 3.3  Isosceles Triangles
• 3.4  Basic Constructions Justified
• 3.5  Inequalities in a Triangle
• 4.1  Properties of a Parallelogram
• 4.2  The Parallelogram and Kite
• 4.3  The Rectangle, Square, and Rhombus
• 4.4  The Trapezoid
• 5.1  Ratios, Rates, and Proportions
• 5.2  Similar Polygons
• 5.3  Proving Triangles Similar
• 5.4  The Pythagorean Theorem
• 5.5  Special Right Triangles
• 5.6  Segments Divided Proportionately
• 6.1  Circles and Related Segments and Angles
• 6.2  More Angle Measures in the Circle
• 6.3  Line and Segment Relationships in the Circle
• 6.4  Some Constructions and Inequalities for the Circle
• 7.1  Locus of Points
• 7.2  Concurrence of Lines
• 7.3  More About Regular Polygons
• 8.1  Area and Initial Postulates
• 8.2  Perimeter and Area of Polygons
• 8.3  Regular Polygons and Area
• 8.4  Circumference and Area of a Circle
• 8.5  More Area Relationships in the Circle
• 9.1  Prisms, Area, and Volume
• 9.2  Pyramids, Area, and Volume
• 9.3  Cylinders and Cones
• 9.4  Polyhedrons and Spheres
• 10.1  The Rectangular Coordinate System
• 10.2  Graphs of Linear Equations and Slope
• 10.3  Preparing to do Analytic Proofs
• 10.4  Analytic Proofs
• 10.5  Equations of Lines
• 11.1  The Sine Ratio and Applications
• 11.2  The Cosine Ratio and Applications
• 11.3  The Tangent Ratio and Other Ratios
• 11.4  Applications with Acute Triangles

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