COURSE DESCRIPTION:

The Geometry course is a comprehensive look at the study of geometric concepts including the basic elements of geometry, proofs, parallel and perpendicular lines, the coordinate plane, triangles, quadrilaterals, polygons, circles, trigonometry, congruence and similarity, surface area, volume and transformations.

COURSE OBJECTIVES:

After completing the course, students will be able to:

• Identify and apply the properties of rays and angles
• Identify and apply the properties of parallel and perpendicular lines
• Write conditional statements
• Write proofs
• Write and graph linear functions
• Identify and apply the properties of triangles
• Identify and apply the properties of quadrilaterals
• Identify and apply the properties of polygons
• Identify and apply the properties of circles
• Prove figures are congruent
• Prove figures are similar
• Apply transformations to various figures

PREREQUISITES:

Algebra I

COURSE LENGTH:

Two semesters

REQUIRED TEXT:

None

COURSE OUTLINE:

UNIT I: Introduction to Geometry
Section 1 - Basic Elements of Geometry
Section 2 - Measuring Segments
Section 3 - Rays and Angles
Section 4 - Parallel and Perpendicular Lines

UNIT II: Introduction to Proof
Section 1 - Inductive and Deductive Reasoning
Section 2 - Conditional Statements and Truth Tables
Section 3 - Informal and Two-Colum Proofs

UNIT III: Parallel Lines and the Coordinate Plane
Section 1 - Parallel Lines and Transversals
Section 2 - The Coordinate Plane
Section 3 - Graphing the Equation of a Line

Unit IV: Triangles
Section 1 - Introduction to Triangles
Section 2 - Congruent Triangles
Section 3 - Isosceles and Equilateral Triangles
Section 4 - Right Triangles and the Pythagorean Theorem
Section 5 - Triangle Inequalities
Section 6 - Perimeter and Area of Triangles
 
UNIT V: Quadrilaterals and Polygons
Section 1 - Squares and Rectangles
Section 2 - Rhombi and Trapezoids
Section 3 - Parallelograms
Section 4 - Polygons

UNIT VI: Similarity
Section 1 - Ratios and Proportions
Section 2 - Similar Triangles
Section 3 - Similar Polygons

UNIT VII: Circles
Section 1 - Arcs and Special Segments
Section 2 - Special Angles in Circles
Section 3 - Equation of a Circle
Section 4 - Circumference and Area of a Circle

UNIT VIII: Right Triangles and Trigonometry
Section 1 - Review of Pythagorean Theorem
Section 2 - Ratios of Right Triangles
Section 3 - Graphing Trigonometric Functions
Section 4 - Law of Sines and Law of Cosines

UNIT IX: Surface Area and Volume
Section 1 - Surface Area and Volume of Prisms and Cylinders
Section 2 - Surface Area and Volume of Pyramids and Cones
Section 3 - Surface Area and Volume of Spheres

UNIT X: Transformations
Section 1 - Translations and Reflections
Section 2 - Rotations and Dilations