Castle Learning Online

Geometry

Castle Learning Online's Geometry is the second of three courses in a series that also includes Algebra and Trigonometry. Hundreds of multiple choice questions are worked out in full detail, with links to hints, reasons, and vocabulary definitions. Reference tables included.

Units: (click to view Sections)

Logic
Sections:
1. Statement & Symbolic Forms
2. Evaluating Statements
3. Constructing Truth Tables
4. Laws of Logic
5. Logical Proofs
The Geometry of Triangles
Sections:
1. Angle Measurement
2. Parallel Lines, Transversals, and Angles
3. Basic Properties of Triangles
4. The Triangle Inequality
5. Interior and Exterior Angles
6. Congruence and Similarity in Triangles
7. Special Properties of Right Triangles
8. Trigonometric Ratios in Right Triangles
The Geometry of Other Figures
Sections:
1. Properties of Quadrilaterals
2. Parallelograms and Rectangles
3. Rhombuses and Squares
4. Trapezoids and Other Polygons
5. Area and Perimeter of Polygons
6. Circles
7. Combinations of Figures
8. 3-Dimensional Figures
9. Locus of Points
10. Constructions Using Compass and Straightedge
Advanced Topics
Sections:
1. Geometric Proofs
2. Inscribed and Central Angles
3. Chords in a Circle
4. Tangents and Secants to a Circle
5. Geometry of a Circle
Introduction to Graphing
Sections:
1. The Real Number Line
2. Coordinate Plane
3. The Equation of a Line
4. Systems of Equations and Inequalities
5. The Slope Equation: Parallel and Perpendicular Lines
6. The Midpoint Formula
7. The Distance Equation
More Graphing Techniques
Sections:
1. The Equation of a Parabola
2. The Equation of a Circle
3. Systems of 1st and 2nd Degree Equations
4. Finding the Area of a Polygon
5. Coordinate Geometry Proofs
6. Ellipses & Hyperbolas
Transformations
Sections:
1. Symmetries and Basic Transformations
2. Applying Transformations
3. Composition of Transformations

Themes:

Mathematical Reasoning
Operations
Modeling and Multiple Representation
Measurement
Patterns and Functions

Attributes:

Diagram
Table
Graph
Word Problem
Proof
Construction