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What is Geometry?

Geometry is the study of space and shape.  It is perhaps the oldest field of mathematics and formal study of it extends back to the time of the ancient Egyptians.  It is important in many fields of study including: engineering, architecture, design, and the sciences, among many others.   The practical ideas of measurement that form part of its core and the logical reasoning that formal geometry uses and helps develop  are very useful.

What will this course be like?

There are 3 main purposes to this course.  The first is to obtain a good background in practical geometry.  The second is to become familiar with logic, methods of proof, and formal mathematics.  The third is to become proficient at solving standardized test questions involving Geometry such as those on the SAT.

Practical Geometry: 

The reason that Geometry is one of the oldest branches of mathematics is because it is practical.  Whenever you need to design, or build anything it is always helpful to measure, and to understand the properties of the shapes that you are forming.  Since it is the mathematics of space and shape, it helps you understand the world around you and motions that objects take in the world.

Logic,methods of proof, and formal mathematics: 

High School Geometry is usually the first introduction to formal mathematics and proof.  It is an important goal of this course to have students not only use the formulas and relationships that they have learned but to understand where they have come from and be able to show that they must be true.

Standardized test questions:   

Most standardized tests that involve mathematics will involve Geometry.  We will be practicing recognizing the Geometry involved in such questions and using the skills developed in the course to solve them.
 

Course Content and approximate pacing

 Semester 1:

    Basics of Geometry (3 weeks)

   Chapter 1

   Introduction to Reasoning and Proof (3 weeks)

    Chapter2

   Perpendicular and Parallel Lines (3 weeks)

   Chapter 3

   Triangle Congruence, Triangle Properties (7 weeks)

   Chapter4

   Chapter 5

Semester 2:

    Quadrilaterals (3.5 weeks)

   Chapter6

   Transformations (3 weeks)

   Chapter 7

    Similarity(2.5 weeks)

   Chapter8

    Right Triangle Trigonometry, Trigonometry with Non-Right Triangles (3 weeks)

   Chapter9

   Additional Materials (non-right triangle trigonometry)

    Circles (3 weeks)

   Chapter 10

    Areas of Polygons and Circles (3 weeks)

   Chapter 11

   Surface Area and Volume (2 weeks)

   Chapter 12