## Geometry

From the times of Ancient Greece and earlier, to 17th century Europe and beyond, humanity’s understanding of geometric principles and relationships has developed into something powerful, beautiful, and applicable. Indeed, this branch of mathematics called Geometry has become fundamental and even essential to everyday life! Students of this course will experience both the development and application of geometry as they explore and interact with topics such as angles, lines, triangles, circles, transformations, and more. Along the way, students will perform constructions in a variety of mediums, analyze and complete deductions and proofs, and apply the geometric principles and theorems that have been discovered over the centuries. Students will also have fun meeting geometry-loving siblings who get into all sorts of adventures and predicaments, which — you guessed it — require geometry to solve.

From beginning to end, the StudyForge Geometry course is set up for student success. Each unit contains numerous interactive explorations that encourage students to discover geometric principles and relationships. Each lesson involves interactive videos that allow students to proceed at their own pace, with the ability to pause and rewind at any point. Additionally, each video is accompanied by a student-friendly note package to encourage deeper engagement and retention. To help students avoid getting stuck and to learn how to solve even the most challenging of geometric problems, all practice questions have detailed solution. Furthermore, students are well prepared for the wide variety of assessments they will encounter, and every quiz and test is randomized to allow retakes and encourage students to strive for mastery. Teachers of the course are equally well resourced, with detailed answer keys to all assessments, a customized dashboard, and supportive analytics to enable them to help all of their students succeed, whatever their skill levels are.

## Table of Contents

Lesson 1: Some Terminology and the Coordinate Plane

Lesson 2: Slope

Lesson 3: The Equation of a Line Part 1: Slope-Intercept Form

Quiz: Review & Warm-up Quiz #1: Lessons 1-3

Lesson 4: The Equation of a Line Part 2: General and Point-Slope Form

Lesson 5: Parallel and Perpendicular Lines

Lesson 6: Distance and Midpoint Formulas

Quiz: Review & Warm-up Quiz #2: Lessons 4-6

Lesson 1: Geometric Constructions

Lesson 2: Bisecting and Other Constructions

Lesson 3: Introduction to Angle Relationships and Terminology

Quiz: Lines and Angles Quiz #1: Lessons 1-3

Lesson 4: Parallel Lines and Transversals – Solving and Reasoning

Lesson 5: Parallel Lines and Transversals – Applications

Quiz: Lines and Angles Quiz #2: Lessons 4 & 5

Quiz: Lines and Angles Practice Test

Quiz: Lines and Angles Test

Quiz: Lines and Angles Test – No Written Work

Lesson 1: Triangle Properties

Lesson 2: Triangle Inequalities

Lesson 3: Triangle Congruence Part I

Quiz: Triangles Quiz #1: Lessons 1-3

Lesson 4: Triangle Congruence Part II

Lesson 5: Triangle Bisectors

Lesson 6: Triangle Medians and Altitudes

Quiz: Triangles Quiz #2: Lessons 4-6

Quiz: Triangles Practice Test

Quiz: Triangles Test

Quiz: Triangles Test – No Written Work

Lesson 1: Polygons and Quadrilaterals

Lesson 2: Parallelograms

Lesson 3: Similarity in Polygons

Quiz: Polygons and Transformations Quiz #1: Lessons 1-3

Lesson 4: Reflections

Lesson 5: Rotations

Lesson 6: Translations

Lesson 7: Dilations

Quiz: Polygons and Transformations Quiz #2: Lessons 4-7

Lesson 8: (Enrichment) Fractals

Quiz: Polygons and Transformations Practice Test

Quiz: Polygons and Transformations Test

Quiz: Polygons and Transformations Test – No Written Work

Lesson 1: Introduction to Trigonometry

Lesson 2: The Three Ratios

Lesson 3: Application of Trigonometric Ratios

Quiz: Trigonometry Quiz #1: Lessons 1-3

Lesson 4: Special Angles and Triangles

Lesson 5: The Sine Law

Lesson 6: The Cosine Law

Quiz: Trigonometry Quiz #2: Lessons 4-6

Quiz: Trigonometry Practice Test

Quiz: Trigonometry Test

Quiz: Trigonometry Test – No Written Work

Lesson 1: Circle Basics and Sectors

Lesson 2: Circle Arcs and Angles

Lesson 3: Circle Intersections

Lesson 4: Circles and Polygons

Lesson 5: Other Circle Geometry Relationships

Lesson 6: Conics: Circles

Lesson 7: (Enrichment) Conics: Parabolas

Lesson 8: (Enrichment) Conics: Ellipses and Hyperbolas

Quiz: Circles Practice Test

Quiz: Circles Test – No Written Work

Quiz: Circles Test

Quiz: Circles Quiz #1: Lessons 1-3

Quiz: Circles Quiz #2: Lessons 4-6

Lesson 1: Perimeter and Area of 2D Shapes – Introduction

Lesson 2: Area of Quadrilaterals

Lesson 3: Area and Perimeter in Composite Figures and the Coordinate Plane

Quiz: Measurement Quiz #1: Lessons 1-3

Lesson 4: Surface Area of Prisms and Pyramids

Lesson 5: Surface Area of Cylinders, Cones, and Spheres

Lesson 6: Volume of 3D Shapes

Lesson 7: Scaling and Proportions

Quiz: Measurement Quiz #2: Lessons 4-7

Lesson 8: (Optional) 3D Representations

Quiz: Measurement Practice Test

Quiz: Measurement Test

Quiz: Measurement Test – No Written Work

Lesson 1: Introduction to Reasoning (Logic)

Lesson 2: Conditional Statements

Lesson 3: Deductive Reasoning

Quiz: Reasoning and Proofs Quiz #1: Lesson 1-3

Lesson 4: Geometric Proofs Part I

Lesson 5: Geometric Proofs Part II

Quiz: Reasoning and Proofs Quiz #2: Lessons 4 and 5

Lesson 6: Circle Property Proofs

Lesson 7: Putting it All Together

Quiz: Reasoning and Proofs Quiz #3: Lessons 6 and 7

Lesson 1: Exploring Data

Lesson 2: More Ways to Represent Data

Lesson 3: Standard Deviation

Lesson 4: The Normal Distribution

Quiz: Statistics Quiz #1: Lessons 1-4

Lesson 5: Simulations

Lesson 6: Statistical Studies

Lesson 7: Estimations and Predictions

Quiz: Statistics Quiz #2: Lessons 5-7

Lesson 8: (Enrichment) Misuse of Statistics

Lesson 9: (Enrichment) Modeling Situations Using Regression

Quiz: Statistics Practice Test

Quiz: Statistics Test

Quiz: Statistics Test – No Written Work

Lesson 1: Sample Space

Lesson 2: Classifying Events

Lesson 3: Classifying Events (Dependent or Independent)

Quiz: Probability Quiz #1: Lessons 1-3

Lesson 4: Conditional Probability

Lesson 5: Expected Value

Quiz: Probability Quiz #2: Lessons 4 and 5

Lesson 6: (Enrichment) The Fundamental Counting Principle

Lesson 7: (Enrichment) Permutations

Lesson 8: (Enrichment) Combinations

Quiz: Probability Practice Test

Quiz: Probability Test

Quiz: Probability Test – No Written Work

Lesson 1: Welcome to your course!

Lesson 2: Teacher Orientation

Lesson 1: START HERE: Welcome to your Course

Lesson 2: Teacher Orientation

## Experience a lesson as your students would

## Don’t Take Our Word for It!

## See What Others Have to Say:

## SONYA

## Online Teacher at EBUS Academy

## Scott

## Blended Teacher at Brampton Christian School

## Alice P

## StudyForge Student

## Ryan J.

## Online Teacher

## Course Features

- Engaging interactives to encourage discovery of principles and theorems
- Intentional elements to increase engagement and enhance interest in topics, such as a narrative storyline, games, historical figure vignettes, emphasis on real-life applications, and more
- Proofs are carefully introduced and scaffolded to enhance accessibility and avoid overwhelming students