Geometry

Pre-Requisites

Algebra I

Description

This sophomore level course is designed to emphasize the study of the properties and applications of common geometric figures in two and three dimensions. It includes the study of transformations and right triangle trigonometry. Inductive and deductive thinking skills are used in writing proofs to solve (prove) properties of geometric figures.

Textbook

Illinois Geometry (Glencoe McGraw-Hill 2010)

Course Outline

Chapter 0 - Preparing for Geometry

Algebraic Expressions

Linear Equations

Linear Inequalities

Ordered Pairs

Systems of Linear Equations

Square Roots and Simplifying Radicals

Chapter 1 - Tools of Geometry

Points, Lines, and Planes

Linear Measure and Precision

Distance and Midpoints

Angle Measure

Angle Relationships

Two-Dimensional Figures

Three-Dimensional Figures

Chapter 2 - Reasoning and Proof

Postulates and Paragraph Proofs

Algebraic Proofs

Proving Segment Relationships

Proving Angle Relationships

Chapter 3 - Parallel and Perpendicular Lines

Parallel Lines and Transversals

Angles and Parallel Lines

Slopes of Lines

Equations of Lines

Proving Lines Parallel

Chapter 4 - Congruent Triangles

Classifying Triangles

Angles of Triangles

Congruent Triangles

Proving Congruence: SSS, SAS

Proving Congruence: ASA, AAS

Isosceles and Equilateral Triangles

Congruence Transformations

Triangles and Coordinate Proofs

Chapter 5 - Relationships in Triangles

Bisectors of Triangles

Medians and Altitudes of Triangles

Inequalities in One Triangle

The Triangle Inequality

Inequalities in Two Triangles

Chapter 6 - Quadrilaterals

Angles of Polygons

Parallelograms

Tests for Parallelograms

Rectangles

Rhombi and Squares

Kites and Trapezoids

Chapter 7 - Proportions and Similarity

Ratios and Proportions

Similar Polygons

Similar Triangles

Parallel Lines and Proportional Parts

Parts of Similar Triangles

Similarity Transformations

Scale Drawings and Model

Chapter 8 - Right Triangles and Trigonometry

Geometric Mean

The Pythagorean Theorem and Its Converse

Special Right Triangles

Trigonometry

Angles of Elevation and Depression

The Law of Sines and Law of Cosines

Chapter 10 - Circles

Circles and Circumference

Measuring Angles and Arcs

Arcs and Chords

Inscribed Angles

Tangents

Secants, Tangents, and Angle Measures

Special Segments in a Circle

Equations of Circles