Geometry (offered in 2019-20)

Taught by Becca Beaman.

Taught by Becca Beaman.

Why study Geometry?

Geometry is one of the foundational subjects in mathematics, and is required to do well on standardized college-entrance exams, such as the SAT and ACT.  The study of geometry includes the understanding of logical reasoning and learning to prove things logically; when we say something is “axiomatic,” we are drawing on our cultural heritage of geometry.  The mental training involved in geometry can change the way you see the world, and can give great insight into the way scientists and mathematicians approach a problem. Geometry is required for many careers, including computer graphic design (animated movies, video games), robotics, medical imaging, architecture, construction, and astronomy.

In our class, we will work to develop the ability to visualize geometric shapes and relationships, as well as to do geometric proofs of theorems.  We will always pull in real-life examples and applications of geometry. We will also cover enough of the basics of trigonometry to enable students to do well on the standardized college-entrance exams.  The class itself will be relatively informal, and every effort will be made to find the humor in the work, and to make sure no student is left behind in the class.

It is interesting that, although geometry is a field of mathematics, it is quite different from arithmetic and algebra; a student who found those subjects challenging may still find they have a gift for geometry.

Course Summary

Geometry is a high school course that covers the basics of geometry while also helping to build the thinking skills of logic, deductive reasoning, analytical reasoning, and problem-solving.  We will develop our ability to visualize objects in space, as well as learning to prove geometric theorems. The course will also cover the basics of trigonometry.

Major Topics Covered

  • Patterns and inductive reasoning

  • Points, lines and planes; angles; perimeter, circumference, area

  • conditional statements

  • definitions and biconditional statements

  • deductive reasoning

  • proving statements about line segments and angles

  • perpendicular and parallel lines

  • congruent triangles; properties of triangles

  • indirect proof; quadrilaterals

  • transformations (motion, reflections, rotations, translations)

  • ratio and proportion

  • proving shapes are similar

  • right triangles and trigonometry

  • circles (tangents, arcs and chords)

  • equations of circles, area of polygons and circles

  • surface area and volume

Major Skills Developed

Students will:

  • Be able to visualize shapes in one, two, and three dimensions

  • Achieve an understanding of the principles of geometry, with an emphasis on how they apply to real-world experiences

  • Be able to distinguish between inductive and deductive reasoning

  • Be able to prove basic geometric theorems

  • Be able to recognize when a theorem has not been proved

  • Be able to solve basic geometry and trigonometry problems, such as those that can be found on the SAT and ACT.

Textbook

Glencoe Geometry, Student Edition, National Edition, by Boyd, Cummins, Malloy, Carter & Flores, (Publisher: McGraw Hill), copyright 2008

ISBN: 9780078738265

 Please make sure you are buying the correct ISBN; this particular ISBN is required. The National Edition is different from the various state editions, and the content and page numbers will differ.