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# Geometry II

## Continue on the road to geometry mastery with this proof-centric course.

This course covers a wide range of theorems in classical Euclidean geometry. You'll start by deriving the Central Angle Theorem and Thales' Theorem, then move on to the Power of a Point Theorem, and conclude with an exploration of different types of triangle centers and their presence on the Euler Line.

Our goal is to help you understand and explore the derivations of these theorems, and to give you many opportunities to practice and strengthen your skills applying them!

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1. 1

### Introduction

Circles form a central part of geometry: get started with your first theorems!

1. #### Central Angles and Arcs

Investigate geometric patterns and proofs that utilize the angles at the center of circles.

2. #### Thales' Theorem

What happens when an angle is inscribed in a semicircle?

3. #### Inscribed Angles

Extend Thales' observation into another beautiful and more general theorem.

2. 2

### In and Out of Circles

Shapes and angles inscribed and circumscribed.

1. Included with

#### Puzzles With Inscribed Angles

Warm up with this round of practice problems that explore the Inscribed Angle Theorem.

2. Included with

Study the properties of quadrilaterals inscribed inside of circles.

3. Included with

#### Power of a Point I

Intersecting lines inside a circle are a special circumstance worth investigating in detail!

4. Included with

#### Intersecting Secants

What happens when lines intersect inside a circle?

3. 3

### Mastering Triangles

Master the inner secrets of triangles.

1. Included with

#### Right Triangles

Start your journey into advanced triangles on the right (aka 90-degree) foot.

2. Included with

#### Thales + Pythagoras

Combine what you know about Thales and Pythagoras to approach some fascinating problems.

3. Included with

#### Cevians

Explore what happens when you connect up one point and one side.

4. Included with

#### Pegboard Triangles

What happens when the triangles are drawn on a regular grid?

4. 4

### Triangle Centers

The Euler Line will blow your mind.

1. Included with

#### Three Different Centers

Learn about the three most commonly used triangle centers and explore how they relate to each other.

2. Included with

#### The Circumcenter

Use perpendicular bisectors to experiment with a fourth type of "center."

3. Included with