Geometry Class Outline
1998-1999

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 Segemnts
• 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
• Two Column Proofs,
• Orienteering

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:
Orthographic, Isometric and Perspective Drawing

Definitions:
Medians, Altitudes, Perpendicular Bisectors

Postulates and Theorems:
SSS, SAS, AAS, SAA, ASA, HL, Isosceles Triangle Theorem Angular Bisectors are made of Equidistant Points

Topics:
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.

Postulates and Theorems:
SAS Inequality Theorem, SSS Inequality Theorem

Topics:

• Largest Sides and Angles of a Triangle
• Range of Possible Triangles

Topics

• Simplifying Ratios
• Using Ratios with Similar Objects
• Scale Factors

Topics:

• AA Similarity Postulate
• Triangle Proportionality Theorem
• Triangle Angle Bisector Theorem

• Geometric Means
• Pythagorean Theorem
• Pythagorean Triples
• Special Right Triangles

• Tangent, Sine and Cosine

Definitions:
Chord, Secant, Tangent, Inscribed, Circumscribed, Point of Tangency, Center, Radius, Diameter, Arc

Topics

• Arc and Central Angles
• Inscribed Angles

Topics

• Tangents from a point to a Circle are Congruent
• Proportions of Intersecting Chords and Secants

Definitions: Locus

Constructions with Compass and Straight Edge:

• 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

Areas of:

• Rectangles
• Squares
• Rhombuses
• Parallelograms
• Trapezoids
• Regular Polygons
• Circles
• Sectors

Topics

• 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
• Midpoint Formula
• Graphing and Writing linear Equations,