Math Fun · Level 3

3.2 Geometric Thinking

Strengthen your geometric intuition and logical reasoning skills through problem solving.

Triangles and Hexagons

Strategic Geometry

Driving on a Polygon

Angle Hunting Axioms

Advanced Mental Shortcuts

Internal Angles in a Polygon

Invariant Angle Sets

Advanced Angle Hunts

The Triangle Inequality

Congruent and Similar Triangles

Bass Fishing

Curry's Paradox

Composite Figure Warm-ups

Adding Lines and Grids

Complementary Areas

Inclusion and Exclusion

Invariant Areas

Angles of Regular Polygons

Is It Regular?

Polygon Areas and Lengths

Matchstick Polygons

Stellations

Dissections

Central Angles and Arcs

Thales's Theorem

Inscribed Angles

Puzzles with Inscribed Angles

Cyclic Quadrilaterals

Power of a Point I

Intersecting Secants

Power of a Point II

Tangents

Problem-Solving Challenges

Right Triangles

Thales + Pythagoras

Cevians

Pegboard Triangles

Three Different Centers

The Circumcenter

Euler's Line

Morley's Triangle

Geometric Stumpers

Challenging Composites

Coordinate Geometry

Advanced Angle Hunting

Applying the Pythagorean Theorem


Course description

In this course, you'll solve delightful geometry puzzles and build a solid foundation of skills for problem-solving with angles, triangles, polygons, and circles. You'll learn how to come up with clever, creative solutions to tough challenges and explore a wide range of theorems. This course is the perfect place to start (or continue) your exploration of geometry if you know how to measure angles and calculate the areas of rectangles, circles, and triangles; and want to learn the next level of geometric problem-solving techniques. Additionally, this is a great course to take if you want to strengthen your geometric intuition in preparation for taking a geometry or design course in school. You'll also need to use a little bit of fundamentals-level algebra in this course, but nothing more advanced than two-variable equations, squares, and square roots.


Topics covered

  • Angle Axioms
  • Angle Hunting Shortcuts
  • Composite Area
  • Complementary Areas
  • Curry's Paradox
  • Invariant Areas
  • Polygon Angles
  • Regular Polygons
  • Stellations
  • The Triangle Inequality
  • Triangle Congruence
  • Triangle Similarity
  • 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

Prerequisites

  • Measurement

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Math Fun · Level 4

4.1 Bayesian Probability

Learn the math behind uncertainty — and how to get rid of it!

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