Geometry

📐 Online Geometry Course – Overview

Course Title: Foundations of Geometry
Format: Fully Online (asynchronous or synchronous)
Duration: 8–12 weeks (customizable)
Level: High School or Introductory College-Level
Prerequisites: Basic algebra skills

🎯 Course Purpose

This course introduces students to the principles and applications of Euclidean geometry. Learners will develop logical reasoning skills, understand geometric relationships, and solve problems using the properties of shapes, angles, and measurements.

🧠 Learning Objectives

By the end of the course, students will be able to:

• Understand basic geometric terms and notation

• Apply properties of angles, lines, triangles, and polygons

• Use formulas to calculate perimeter, area, and volume

• Work with congruence, similarity, and transformations

• Prove geometric theorems using deductive reasoning

• Apply geometry to real-world and problem-solving contexts

📝 Course Content Breakdown

Module 1: Introduction to Geometry

• Points, lines, planes, and angles

• Types of angles and angle relationships

• Measuring angles with a protractor

• Basic constructions with compass and straightedge (optional)

Module 2: Reasoning and Proof

• Inductive vs. deductive reasoning

• Conditional statements and logic

• Writing geometric proofs

• Properties of equality and congruence

Module 3: Parallel and Perpendicular Lines

• Angle pairs formed by transversals

• Properties of parallel lines

• Equations of parallel and perpendicular lines

• Coordinate geometry: slope and distance

Module 4: Triangles

• Classification of triangles

• Triangle inequality theorem

• Congruent triangles and triangle congruence (SSS, SAS, ASA, AAS)

• Triangle theorems (base angles, exterior angles)

• Special segments (medians, altitudes, bisectors)

Module 5: Quadrilaterals and Polygons

• Properties of parallelograms, rectangles, rhombuses, squares, and trapezoids

• Interior and exterior angles of polygons

• Coordinate geometry applications

Module 6: Similarity and Proportions

• Ratios and proportions

• Similar polygons

• Triangle similarity (AA, SSS, SAS)

• Indirect measurement

Module 7: Circles

• Arcs, chords, central and inscribed angles

• Tangents, secants, and circle theorems

• Area and circumference

• Sector area and arc length

Module 8: Area, Surface Area, and Volume

• Area formulas for 2D shapes

• Surface area and volume of 3D shapes: prisms, cylinders, cones, spheres, pyramids

• Composite figures and real-world applications

Module 9: Transformations and Symmetry

• Translations, rotations, reflections, dilations

• Symmetry and tessellations

• Transformations in the coordinate plane