Interactive course — Foundational Math

Geometry II

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

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Overview

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!

Topics covered

  • Centroid
  • Circumcenter
  • Cyclic Quadrilateral Theorem
  • Euler's Line
  • Incenter
  • Inscribed Angles
  • Intersecting Chord Theorem
  • Intersecting Secants Theorem
  • Intersecting Tangent Theorem
  • Orthocenter
  • Power of a Point Theorem

Interactive quizzes

17

Concepts and exercises

145+

Course map

Prerequisites and Next Steps

  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.

      1
    2. Thales' Theorem

      What happens when an angle is inscribed in a semicircle?

      2
    3. Inscribed Angles

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

      3
  2. 2

    In and Out of Circles

    Shapes and angles inscribed and circumscribed.

    1. Puzzles With Inscribed Angles

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

      4
    2. Cyclic Quadrilaterals

      Study the properties of quadrilaterals inscribed inside of circles.

      5
    3. Power of a Point I

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

      6
    4. Power of a Point II

      Solve a problem assortment that puts all of your new theorems to use!

      7
    5. Tangents

      What happens when lines just barely touch the outside of a circle?

      8
    6. Problem Solving Challenges

      Practice and strengthen the entire set of tools you've learned so far with this final round of challenges.

      9
  3. 3

    Mastering Triangles

    Master the inner secrets of triangles.

    1. Right Triangles

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

      10
    2. Thales + Pythagoras

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

      11
    3. Cevians

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

      12
    4. Pegboard Triangles

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

      13
  4. 4

    Triangle Centers

    The Euler Line will blow your mind.

    1. Three Different Centers

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

      14
    2. The Circumcenter

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

      15
    3. Euler's Line

      Prove a profound result that relates the orthocenter, centroid, and circumcenter.

      16
    4. Morley's Triangle

      Use trisectors rather than bisectors to get an astonishing result.

      17