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Honors Geometry

Prerequisites: Qualifying math score and completion of Algebra I or equivalent

Course Format: Individually Paced

Course Length: Typically 6 months

Recommended School Credit: 1.0 credit

Course Code: GEO

Course Description

Description

This proof-based geometry course, based on a popular classic textbook, covers concepts typically offered in a full-year honors geometry course. To supplement the lessons in the text book, videos, online interactives, assessments and projects provide students an opportunity to develop mathematical reasoning, critical thinking skills, and problem solving techniques to investigate and explore geometry. Additionally, students are introduced to a dynamic software tool, GeoGebra, through projects that they create.

The textbook must be purchased separately by the student.

Topics include:

  • Deductive and inductive reasoning
  • Direct and indirect proof
  • Parallel lines and planes
  • Congruence and similarity
  • Polygons
  • Perimeter, area, and volume
  • Right triangles
  • Circles
  • Coordinate geometry
  • Transformations and symmetry
  • Constructions and Loci

Materials Needed

There is a textbook purchase required for this course:

Geometry, 2000 edition by Jurgensen, Brown, & Jurgensen; McDougal Litell.   ISBN: 0395977274

A compass is required in addition to the textbook.

Geometry textbook cover Compass

List of Topics

Upon successful completion of the course, students will be able to demonstrate mastery over the following topics:

Points, Lines, Planes, & Angles

  • A Game and Some Geometry
  • Points, Lines, and Planes
  • Segments, Rays, and Distance
  • Angles
  • Postulates and Theorems Relating Points, Lines and Planes

Deductive Reasoning

  • If-Then Statements; Converses
  • Properties from Algebra
  • Proving Theorems
  • Special Pairs of Angles
  • Perpendicular Lines
  • Planning a Proof
  • Flowchart and Paragraph Proofs

Parallel Lines and Planes

  • Definitions
  • Properties of Parallel Lines
  • Proving Lines Parallel
  • Angles of a Triangle
  • Angles of a Polygon
  • Inductive Reasoning

Congruent Triangles

  • Congruent Figures
  • Some Ways to Prove Triangles are Congruent
  • Using Congruent Triangles
  • Isosceles Triangle Theorems
  • Other Methods of Proving 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
  • Applications of Right Triangle Trigonometry
  • Law of Sines and Law of Cosines

Circles

  • Basic Terms
  • Tangents
  • Arcs and Central Angles
  • Arcs and Chords
  • Inscribed Angles
  • Other Angles
  • 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 Rhombuses
  • 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 Volume of Similar Solids

Coordinate Geometry

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

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Sample Video Lecture

Sample Video

Sample video lecture


Sample GeoGebra Interactive

Geogebra interactive

System Requirements

CTYOnline courses require a properly-maintained computer with Internet access and a recent-version web browser (such as Firefox, Safari, or Internet Explorer) with the Adobe Flash plugin. Students are expected to be familiar with standard computer operations (e.g. login, cut & paste, email attachments, etc).

This course uses an online classroom for individual or group discussions with the instructor. The classroom works on standard computers with the Adobe Flash plugin, and also tablets or handhelds that support the Adobe Connect Mobile app.