GEOMETRY

Points, Lines, Planes and Angles

  1. Introduction to Geometry

  2. Points, Lines, and Planes

  3. Segments, Rays, and distance

  4. Angles

  5. Postulates and Theorems Relating Points, Lines, and Planes

Deductive Reasoning

  1. If-Then Statements; Converses

  2. Properties from Algebra

  3. Proving Theorems

  4. Special Pairs of Angles

  5. Perpendicular Lines

  6. Planning a Proof

Parallel Lines and Planes

  1. Definitions

  2. Properties of Parallel Lines

  3. Proving Lines Parallel

  4. Angles of a Triangle

  5. Angles of a Polygon

  6. Inductive Reasoning

Congruent Triangles

  1. Congruent Figures

  2. Some Ways to Prove Triangles Congruent

  3. Using Congruent Triangles

  4. The Isosceles Triangle Theorems

  5. Other Methods of Proving Triangles Congruent

  6. Using More than One pair of Congruent Triangles

  7. Medians, Altitudes, and Perpendicular Bisectors

Quadrilaterals

  1. Properties of Parallelograms

  2. Ways to Prove that Quadrilaterals are Parallelograms

  3. Theorems Involving Parallel Lines

  4. Special Parallelograms

  5. Trapezoids

Inequalities in Geometry

  1. Inequalities

  2. Inverses and Contrapositives

  3. Indirect Proof

  4. Inequalities for One Triangle

  5. Inequalities for Two Triangles

Similar Polygons

  1. Ratio and Proportion

  2. Properties of Proportions

  3. Similar Polygons

  4. A Postulate for Similar Triangles

  5. Proportional Lengths

Right Triangles

  1. Similarity in Right Triangles

  2. The Pythagorean Theorem

  3. The Converse of the Pythagorean Theorem

  4. A Postulate for Similar Triangles

  5. Special Right Triangles

  6. The Tangent Ratio

  7. The Sine and Cosine Ratios

  8. Applications of Right triangle Trigonometry

Circles

  1. Basic Terms

  2. Tangents

  3. Arcs and Central Angles

  4. Arcs and Chords

  5. Inscribed Angles

  6. Other Angles

  7. Circles and Lengths of Segments

Constructions and Loci

  1. What Construction Means

  2. Perpendiculars and Parallels

  3. Concurrent Lines

  4. Circles

  5. Special Segments

  6. The Meaning of Locus

  7. Locus Problems

  8. Locus and Construction

Areas of Plane Figures

  1. Areas of Rectangles

  2. Areas of Parallelograms, Triangles, and Rhombuses

  3. Areas of Trapezoids

  4. Areas of Regular Polygons

  5. Circumferences and Areas of Circles

  6. Arc Lengths and Areas of Sectors

  7. Ratio of Areas

  8. Geometric Probability

Areas and Volumes of Solids

  1. Prisms

  2. Pyramids

  3. Cylinders and Cones

  4. Spheres

  5. Areas and Volumes of Similar Solids

Coordinate Geometry

  1. The distance Formula

  2. Slope of a Line

  3. Parallel and Perpendicular lines

  4. A Postulate for Similar Triangles

  5. Vectors

  6. The Midpoint Formula

  7. Graphing Linear Equations

  8. Writing Linear Equations

  9. Organizing Coordinate Proofs

  10. Coordinate geometry Proofs

Transformations

  1. Mappings and functions

  2. Reflections

  3. Translations and Glide Reflections

  4. Rotations

  5. Dilations

  6. Composites of Mappings

  7. Inverses and the Identity

  8. symmetry in the Plane and in Space