Definitions:
- Postulates, Axioms, Theorems
- Point, Line, Ray, Segment,
- Equidistant,
- Colinear and Coplanar,
- Straight angle, Right Angle,
- Bisector and Midpoint
- Vertex and Sides of an Angle
- Intersection,
- Adjacent Angles,
- Degree, Radian, Grad
Topics:
Measuring Angles, Angle Addition Postulate, Optical Illusions
Constructions with Compass and Straight Edge:
- Copying Angles and Segments
- Bisecting Angles and Segments
- Constructing Perpendicular and Parallel Segments
- Golden Proportion and Golden Spiral
Postulates and Theorems:
- Addition Property of Equations
- Subtraction Property of Equations,
- Division Property of Equations,
- Multiplicative Property of Equations,
- Substitution Property,
- Reflexive Property,
- Symmetric Property of Equations,
- Transitive Property,
- Midpoint Theorem and Angle Bisector Theorem,
- Supplementary Angles and Complementary Angles
- Perpendicularity
- Vertical Angles
Topics:
- Conditional Statements,
- Truth Tables,
- Two Column Proofs,
- Orienteering,
- Logic Puzzles
Definitions:
- Parallel,
- Congruent,
- Transversal,
- Alternate Interior Angles,
- Same Side Interior Angles,
- Corresponding Angles,
- Interior and Exterior Angles of Polygons
Postulates and Theorems:
- "Corr", "AI", "SSI"
- The Lines of Intersection of Parallel Planes are Parallel
- Through a line and a non-colinear point exist exactly one parallel line and exactly one perpendicular line
- Interior Angles of a Triangle add up to 180°
- Exterior angle of a Triangle equals the sum of its remote interior angles
- The Sum of Interior and Exterior Angles of a Regular Convex Polygon.
Topics:
Technical Drawing, Inductive Reasoning
Definitions:
Medians, Altitudes, Perpendicular BisectorsPostulates and Theorems:
SSS, SAS, AAS, SAA, ASA, HL, Isosceles Triangle Theorem Angular Bisectors are made of Equidistant PointsTopics:
Notation, Strategies in Proofs
Definitions:
- Quadrilateral
- Parallelogram
- Rhombus
- Rectangle
- Square
- Trapezoid
- The Bases, Legs and the Median of A Trapezoid
Postulates and Theorems:
- Opposite Sides and Angles of a Parallelogram are Congruent,
- Diagonals of Parallelograms bisect each other
- Diagonals of Rectangles are Congruent
- Diagonals of Rhombuses are Perpendicular
- Diagonals of Rhombuses Bisect Opposite Angles
- The Median of A Trapezoid is Equal to Half the Sum of the Bases
- If Congruent Segments are Cut Across Parallel Lines on One Transversal, then Congruent Segments are Cut on Every Transversal
- A Segment Between the Midpoints of Two Sides of a Triangle is parallel and Half the Length of the Third Side.
Topics:
Braces and Trusses, Drawing Shapes using Mathematica.
Definitions:
Contrapositive, Converse, and Inverses of Conditional StatementsPostulates and Theorems:
SAS Inequality Theorem, SSS Inequality TheoremTopics:
- Indirect Proofs (Proof By Contradiction)
- Largest Sides and Angles of a Triangle
- Range of Possible Triangles
- Shortest Path Problems
- Non-Euclidian Geometries
Topics
- Simplifying Ratios
- Using Ratios with Similar Objects
- Scale Factors
Topics:
- AA Similarity Postulate
- Triangle Proportionality Theorem
- Triangle Angle Bisector Theorem
- Intro to Topology
- Geometric Means
- Pythagorean Theorem
- Pythagorean Triples
- Special Right Triangles
- Tangent, Sine and Cosine
- Applications
- Law of Sines
- Law of Cosines
Definitions:
Chord, Secant, Tangent, Inscribed, Circumscribed, Point of Tangency, Center, Radius, Diameter, ArcTopics
- Arc and Central Angles
- Inscribed Angles
Topics
- Tangents from a point to a Circle are Congruent
- Proportions of Intersecting Chords and Secants
Definitions: LocusConstructions with Compass and Straight Edge:
Topics
- Finding the point Equidistant from the sides of a Triangle
- Finding the point Equidistant from the vertices of a Triangle
- Finding the Center of Gravity
- Circumscribing and Inscribing Circles in a Triangle
- Construction Regular Polygons
- Trisecting a Segment
- Constructing a Proportional Segment
- Constructing the Geometric Mean of a Segment
- Locus Problems
- Nine point Circle
Areas of:
Topics
- Rectangles
- Squares
- Rhombuses
- Parallelograms
- Trapezoids
- Regular Polygons
- Circles
- Sectors
- Arc Lengths
- Area of Similar Objects in a Plane
- Geometric Probability
Areas and Volumes of
- Prisms
- Pyramids
- Cylinders
- Cones
- Spheres
- Similar Solids
Topics:
- Distance Formula
- Slope of a line
- Parallel and Perpendicular Lines,
- Vectors,
- Midpoint Formula
Topics:
- Graphing and Writing linear Equations,
- Co-ordinate Proofs,
- Steiner's Problem
Topics:
- Mapping and Functions
- Reflections
- Translations
- Rotations
- Dilations
- Computer Animations
- Composites of Mappings
- Inverses
- Symmetry, Tessellations, and Fractals