Interactive course — Foundational Math

Geometry I

Build a foundation for geometry with angles, triangles, and polygons.

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Overview

In this course, you'll solve delightful geometry puzzles and build a solid foundation of skills for problem-solving with angles, triangles, and polygons. You'll also improve your visual intuition and learn how to come up with clever, creative solutions to tough challenges.

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.

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

Interactive quizzes

23

Concepts and exercises

170+

Course map

Prerequisites and Next Steps

  1. 1

    Introduction

    Get started with 2D on a journey with polygons and clever geometry puzzles.

    1. Triangles and Hexagons

      Get started by thinking about patterns that combine triangles and hexagons.

      1
    2. Strategic Geometry

      Work out strategies to approach these area challenges.

      2
    3. Driving on a Polygon

      Derive a fundamental theorem of geometry!

      3
  2. 2

    Angles

    Beware: even a cute little angle can bite!

    1. Angle Hunting Axioms

      Practice finding missing angles.

      4
    2. Advanced Mental Shortcuts

      Learn sneaky strategies for solving tough angle problems.

      5
    3. Internal Angles in a Polygon

      Solve angle problems involving polygons that have many sides.

      6
    4. Invariant Angle Sets

      Investigate scenarios where the sum of several angles stays constant.

      7
    5. Advanced Angle Hunts

      Tackle this last set of angle challenges by combining all of the techniques you've learned so far.

      8
  3. 3

    Triangles

    Endless complexity can come from just three sides.

    1. The Triangle Inequality

      In what circumstances can you make a triangle?

      9
    2. Congruent and Similar Triangles

      When are triangles the same?

      10
    3. Bass Fishing

      Investigate a special case where a triangle can be drawn two ways.

      11
    4. Curry's Paradox

      Uh... Where did the missing square go?

      12
  4. 4

    Composite Polygons

    Celebrate the surprising truths inherent to the mathematics of space.

    1. Warm-ups

      Warm up your problem-solving muscles by exploring these shape-combining diagrams.

      13
    2. Adding Lines and Grids

      Add lines to help clarify your thinking.

      14
    3. Complementary Areas

      Sometimes it's easier to find the area of what's left after your shape is removed...

      15
    4. Inclusion and Exclusion

      What happens when shapes overlap?

      16
    5. Invariant Areas

      When bend, stretch, move and spin parts of these figures, the areas change shape but don't change size.

      17
  5. 5

    Regular Polygons

    From perimeters and pi to stellations and tessellations.

    1. Angles of Regular Polygons

      When all of the sides are the same length and all of the angles are the same measure, what else must be true?

      18
    2. Is It Regular?

      Can you be absolutely certain that each of these polygons is regular?

      19
    3. Polygon Areas and Lengths

      Apply the Pythagorean Theorem to find length and area measures of regular polygons.

      20
    4. Matchstick Polygons

      Play around with these polygons made out of matchsticks, q-tips, and toothpicks.

      21
    5. Stellations

      By extending all of the edges of a polygon you can make beautiful stars.

      22
    6. Dissections

      Practice your skills polygon problem-solving with these dissected polygon puzzles.

      23