Geometry

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Welcome to the Geometry course page. Below you will find the course outline and the section texts that will be used throughout the course. Geometry is designed as a one-semester rigorous course in Euclidian Geometry, and will prepare you for your subsequent Algebra II and Trigonometry courses.

The word geometry originally comes from Greek (geo meaning world, metri meaning measure) and means, literally, to measure the earth. It is an ancient branch of mathematics, but its modern meaning depends largely on context; however, geometry largely encompasses forms of non-numeric mathematics, such as those involving measurement, area and perimeter calculation, and work involving angles and position. It was one of the two fields of pre-modern mathematics, the other being the study of numbers. In modern times, geometric concepts have been generalized to a high level of abstraction and complexity, and have been subjected to the methods of calculus and abstract algebra, so that many modern branches of the field are barely recognizable as the descendants of early geometry. This Wikibook is dedicated to high school geometry and geometry in general.

The course syllabus for Geometry can be accessed and downloaded here: Geometry Course Syllabus

Contents

Course Oultine

Unit 1 - Geometry Essentials

  1. Points, Lines, & Planes
  2. Equal, Congruent, or Similar
  3. Midpoint & Distance Formulas
  4. Angles
  5. Angle Pair Relationships
  6. Polygons
  7. Perimeter, Circumference, & Area

Unit 2 - Reasoning & Proof

  1. Inductive and Deductive Reasoning
  2. Conditional Statements & Symbolism
  3. Laws of Syllogy and Detachment
  4. Properties of Equality

Unit 3 - Parallel & Perpendicular Lines

  1. Pairs of Lines & Angles
  2. Parallel Lines & Transversals
  3. Prove Lines Are Parallel
  4. Finding & Using Slopes of Lines
  5. Write & Graph Equations of Lines

Unit 4 - Congruent Triangles

  1. Triangle Sum Properties
  2. Triangles & Congruence
  3. SSS
  4. SAS & HL
  5. ASA and AAS
  6. Isosceles & Equilateral Triangles

Unit 5 - Triangle Relationships

  1. Midsegment Theorem
  2. Coordinate Proof
  3. Perpendicular Bisectors
  4. Angle Bisectors
  5. Medians & Altitudes
  6. Triangle Inequalities

Unit 6 - Similarity

  1. Ratios, Proportions, & Geometric Mean
  2. Use Proportions to Solve Geometry Problems
  3. Similar Polygons
  4. Similar Triangles with AA
  5. Similar Triangles with SSS & SAS

Unit 7 - Right Triangles & Trigonometry

  1. The Pythagorean Theorem
  2. Converse of the Pythagorean Theorem
  3. Similar Right Triangles
  4. Special Right Triangles
  5. Sine, Cosine, & Tangent Ratios
  6. Solving Right Triangles

Unit 8 - Quadrilaterals

  1. Angle Measures in Polygons
  2. Parallelograms
  3. Rhombuses, Rectangles, & Squares
  4. Trapezoids & Kites
  5. Special Quadrilaterals

Unit 9 - Circles

  1. Properties of Tangents
  2. Arc Measures
  3. Properties of Chords
  4. Inscribed Angles
  5. Angle Relationships in Circles
  6. Segment Lengths in Circles
  7. Equations of Circles

Unit 10 - Areas

  1. Areas of Triangles & Parallelograms
  2. Areas of Trapezoids, Rhombuses, & Kites
  3. Area & Perimeter of Similar Figures
  4. Areas of Circles & Sectors

Unit 11 - Surface Area & Volume

  1. Exploring Solids
  2. Surface Area of Prisms & Cylinders
  3. Surface Area of Pyramids & Cones
  4. Volume of Prisms & Cylinders
  5. Volume of Pyramids & Cones
  6. Surface Area & Volume of Spheres

Unit 12 - Transformations

  1. Vectors
  2. Translations
  3. Reflections
  4. Rotations
  5. Compositions of Transformations
  6. Dilations

Appendix

  1. Postulates & Definitions
  2. Formulas & Equations

Projects

  1. Baloons & Linear Regression - Inflating baloons and fitting a linear, quadratic, or exponential line to the data.
  2. Polling Peers - Using SurveyMonkey to develop a survey to give to student peers and evaluate the data.
  3. Finding Π with Pizza - Students will measure actual circumference and diameter of pizzas and determine best buys.
  4. Stock Market Mark-It - Students will select a company they have an interest in and evaluate it over time.
  5. M&M's and Probability - Students will evaluate a pack of M&M's for colors content, and determine probabilities based on their data.
  6. Candy Box - Students will receive a box of candy and use it to find surface area and volume.
  7. Bottle Rocketry - Students will construct a bottle rocket out of common household items and a soda pop bottle and evaluate it's flight.

Online Activities

  1. Arithmetic Four
  2. Crossword Puzzle
  3. Memory Game
  4. Angle Pair Relationships
  5. Road Trip 1
  6. Road Trip 2
  7. Road Trip 3
  8. Road Trip 4
  9. Deep Sea Diving
  10. Mummy Chase
  11. Planet Blaster
  12. Equation Buster - Click here for more levels
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