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# Geometry (offered in 2019-20)

## 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

*Geometry** *by Larson, Boswell, and Stiff (Publisher: Mcdougall Littell)

Publication Date: 2004 (10th Edition)

ISBN-10: 0618250220

ISBN-13: 978-0618250226

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Prerequisite: Mastery of basic math skills (see list below)

**and completion of Algebra I**Assessment Test and Parent Questionnaire requested prior to beginning (see bottom of page for links)

This high school tutorial will introduce students to logic as the basis of formal and informal proofs. Since topics build upon one another, students will need to strive for mastery and retention of concepts. Periodic reviews of algebraic skills are included in the curriculum. The class will proceed at a solid pace in order to cover the material while only meeting for three hours each week. Therefore, good homework habits will be necessary in order for students to keep up with the class.

## PREREQUISITES

Following is a list of pre-Algebra math skills that should be fully mastered before taking a high school math course. The ones in the "critical" list are often inadequate in homeschooled students:

### CRITICAL SKILLS

Basic multiplication facts with some speed (through 12’s)

Order of operations

Fractions: performing all 4 operations; converting to mixed numbers and decimals

Decimals: performing operations; rounding; conversion to fractions; terminating vs. non-terminating

Percents

Setting up proportions (e.g. in word problems)

Exponents: evaluating; performing operations

Area, perimeter/circumference, volume

### IMPORTANT SKILLS

Unit conversions (simple)

Computing simple averages

Working with the concept of rates (e.g. price per lb., speed, etc.)

Word problems with any of the above

## ASSESSMENT AND QUESTIONNAIRE

An assessment test of previous math skills and a parent questionnaire are required before students may enter this course.

## BOOK

**Geometry*** by Larson, Boswell, and Stiff (Publisher: Mcdougall Littell)Publication Date: 2004 (10th Edition)*

**ISBN-10: 0618250220****ISBN-13: 978-0618250226**