Geometry Topics

Points, Lines, Planes, and Angles
Undefined Terms
Segments, Rays, and Distance
Angles
Postulates and Theorems Relating Points, Lines, and Planes

Deductive Reasoning
If-Then Statements and Converses
Properties from Algebra
Proving Theorems
Special Pairs of Angles
Perpendicular Lines
Planning a Proof

Parallel Lines and Planes
Introduction to Parallel Lines and Planes
Properties of Parallel Lines
Proving Lines Parallel
Angles of a Triangle
Angles of a Polygon
Inductive Reasoning

Congruent Triangles
Congruent Figures
Proving Triangles Congruent
Using Congruent Triangles
The Isosceles Triangle Theorems
Other Ways to Prove Triangles Congruent
Extraneous Ways to Prove Triangles Congruent
Using More Than One Pair of Congruent Triangles
Medians, Altitudes, and Perpendicular Bisectors

Quadrilaterals
Properties of Parallelograms
Ways to Prove that Quadrilaterals are Parallelograms
Theorems Involving Parallel Lines
Special Parallelograms
Trapezoids

Inequalities in Geometry
Inequalities
Inverses and Contrapositives
Indirect Proof
Inequalities for One Triangle
Inequalities for Two Triangles

Similar Polygons
Ratio and Proportion
Properties of Proportions
Similar Polygons
A Postulate for Similar Triangles
Theorems for Similar Triangles
Proportional Lengths

Right Triangles
Similarity in Right Triangles
The Pythagorean Theorem
The Converse of the Pythagorean Theorem
Special Right Triangles
The Tangent Ratio
The Sine and Cosine Ratios
The Law of Sines
The Law of Cosines
Applications of Right Triangle Trigonometry

Circles
Basic Terms
Tangents
Arcs and Central Angles
Arcs and Chords
Inscribed Angles
Angles in the Interior and Exterior of Circles
Circles and Lengths of Segments

Constructions and Loci
What Construction Means
Perpendiculars and Parallels
Concurrent Lines
Circles
Special Segments
The Meaning of Locus
Locus Problems
Locus and Construction

Areas of Plane Figures
Areas of Rectangles
Areas of Parallelograms, Triangles, and Rhombi
Areas of Trapezoids
Areas of Regular Polygons
Circumferences and Areas of Circles
Arc Lengths and Areas of Sectors
Ratios of Areas
Geometric Probability

Areas and Volumes of Solids
Prisms
Pyramids
Cylinders and Cones
Spheres
Areas and Volumes of Similar Solids

Coordinate Geometry
The Distance Formula and Equations of Circles
Slope of a Line
Parallel and Perpendicular Lines
Vectors
The Midpoint Formula
Graphing Linear Equations
Writing Linear Equations
Organizing Coordinate Proofs

Coming soon:
Coordinate Geometry Proofs

Transformations
Mappings and Functions
Reflections
Translations and Glide Reflections
Rotations
Dilations
Composites of Mappings
Inverses and the Identity
Symmetry in the Plane and in Space